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REVIEW 3 major objections 3 minor 110 references

Universal fluctuations of localized two interacting particles in one dimension

T0 review · 3 major / 3 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Localized two-particle wavefunctions in a 1D disordered chain show fluctuation growth $r^{1/2}$ with random potentials alone and $r^{1/3}$ (the $(1+1)$D KPZ exponent) once random long-range interactions decorrelate Fock-space site energies.

desk verdict Nice crossover in TIP Fock-space fluctuations, but the FSA-to-DP mapping drops the common energy denominator and the KPZ claim needs distributional support. read the letter →

arxiv 2502.01399 v1 pith:UZ75URVN submitted 2025-02-03 cond-mat.dis-nn cond-mat.quant-gascond-mat.stat-mechquant-ph

Sen Mu , Gabriel Lemarié , Jiangbin Gong This is my paper · ORCID
classification cond-mat.dis-nncond-mat.quant-gascond-mat.stat-mechquant-ph
keywords twointeractingparticlesFock-spacegraphAndersonlocalizationdirectedpolymerKardar-Parisi-Zhanguniversalityrandomlong-rangeinteractionsfluctuationgrowthexponentforwardscatteringapproximation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks how the sample-to-sample fluctuations of a localized two-particle wavefunction behave when the wavefunction is viewed in Fock space, the graph whose sites are two-particle configurations and whose edges are single-particle hops. The central claim is that the growth of the fluctuation with graph distance $r$ is set by the correlation structure of the disorder: a random potential alone yields correlated site energies and $\sigma[\ln|\psi_{\rm loc}(r)|^2]\sim r^{1/2}$, while random long-range interactions decorrelate those energies and drive the exponent to $1/3$, the $(1+1)$-dimensional Kardar-Parisi-Zhang value. The argument is carried by the forward-scattering approximation, which turns the wavefunction amplitude into a sum over directed paths, i.e., into the partition function of a complex directed polymer. The same $1/2\to1/3$ crossover is reproduced in a directed polymer model with competing columnar and point disorder, and the authors take this as evidence that disorder structure, not just disorder strength, controls fluctuation universality in the Fock space of disordered quantum systems.

What carries the argument

The central object is the Fock-space graph of two spinless fermions on a one-dimensional chain, an upper-triangular slice of a square lattice with the diagonal excluded, in which each site labels a two-particle configuration and edges are single-particle hops. The load-bearing identity is the forward-scattering approximation, $\psi_X(P)=\sum_{\text{directed paths }Q\to P}\prod_{l=1}^{r}T/(E_Q-E_{S_l})$, which expresses the localized amplitude at graph distance $r$ as a sum over directed paths and thereby identifies $\ln|\psi_{\rm loc}(r)|^2$ with the free energy of a $(1+1)$-dimensional directed polymer carrying complex site weights. The power of the identity is that the Fock-space on-site energies $E_S$ inherit two distinct disorder structures: columnar disorder $V_c(i,j)=V_i+V_j$ from the random potential, with covariance $\mathrm{Cov}[V_c(i,j),V_c(k,l)] = (W_V^2/12)(\delta_{i,k}+\delta_{i,l}+\delta_{j,k}+\delta_{j,l})$, and uncorrelated point disorder from random long-range interactions. A controlled check is provided by a directed polymer model with disorder $\gamma V_p+(1-\gamma)V_c$ evolved by the transfer matrix $Z(x,y+1)=e^{-iV(x,y+1)}[Z(x-1,y)+Z(x+1,y)]$, whose free-energy fluctuations reproduce the same $1/2$-to-$1/3$ crossover.

What would settle it

Decisive check: simulate the full time evolution (not the forward-scattering approximation) for $L=512$, $W_V=10$, $W_D=30$, $\alpha=0$ at $t=500$, and measure the local slope of $\log\sigma[\ln|\psi_{\rm loc}(r)|^2]$ versus $\log r$ over $r\in[10,256]$. If the local slope drifts away from $1/3$ toward $1/2$ as $r$ grows, the claimed KPZ universality is a finite-size crossover; if it remains at $1/3$ across the available decade, the claim survives.

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Extended reading notes

Core claim

The authors' central discovery is a universal, disorder-structured scaling law for localized two-particle wavefunctions in a one-dimensional disordered chain: at fixed graph distance $r$ in Fock space, $\sigma[\ln|\psi_{\rm loc}(r)|^2]\sim r^{\beta}$, with $\beta\approx1/2$ for random potentials only and $\beta\approx1/3$ once random long-range interactions dominate. The random potential maps to columnar disorder on the Fock-space lattice, site energies of the form $V_i+V_j$ whose correlations never decay with distance, while the random long-range interactions map to point disorder. The crossover is controlled by the relative disorder strengths $W_V$ and $W_D$ and by the power-law decay exponent $\alpha$ of the interactions; numerically, $\beta\simeq1/3$ survives up to $\alpha\simeq0.2$ and then crosses back toward $1/2$ as $\alpha$ approaches $0.8$. In the authors' reading, the $1/2$ regime is an effective one-dimensional Anderson behavior even though the Fock-space graph is two-dimensional, and the $1/3$ regime is genuine $(1+1)$D KPZ universality. The same crossover in the companion directed polymer calculation with $\gamma V_p+(1-\gamma)V_c$ is presented as confirmation that the correspondence between physical disorder types and Fock-space disorder structures is universal.

Load-bearing premise

The argument stands on the assumption that only the shortest non-backtracking paths between two configurations contribute, so the two-particle wavefunction is exactly a directed polymer; if longer or looping paths matter, the deduced 1/3 exponent may not describe the full system.

Editorial extensions

If this is right

  • In the strong-disorder regime, two interacting particles without random long-range interactions should show $\sigma[\ln|\psi_{\rm loc}(r)|^2]\sim r^{1/2}$ in Fock space, the same fluctuation growth as one-dimensional Anderson localization despite the two-dimensional graph.
  • Adding random long-range interactions that are strong or slowly decaying (numerically $\alpha\lesssim0.2$ for $W_V=10$, $W_D=30$) moves the system into the $(1+1)$D KPZ universality class, with $\sigma\sim r^{1/3}$.
  • The exact correspondence inferred from the companion directed polymer model is: random potential equals columnar disorder, random long-range interaction equals point disorder; consequently the fluctuation exponent is a diagnostic that can distinguish these disorder structures in experiments.
  • For more than two particles, random two-body interactions cannot fully decorrelate the Fock-space site energies, because there are only $L(L-1)/2$ interaction pairs but $C(L,N)$ Fock-space sites; the paper concludes that correlated-disorder effects persist in that regime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct extension the authors do not state: the same $r^{1/3}$ sample-to-sample scaling should appear in the eigenstate amplitudes themselves, not only in the quench dynamics at $t=500$, so exact diagonalization of the TIP Hamiltonian in Fock space would provide an independent check.
  • The columnar-disorder picture implies that in the $W_D=0$ case the localized wavefunction is pinned to an optimal column of the Fock-space graph; single-site readout of one particle's conditional position as a function of graph distance could reveal that pinning.
  • Because the quoted exponent is extracted from fluctuations at one fixed time, temporal fluctuations may contaminate the measurement; a systematic check of how $\sigma[\ln|\psi_{\rm loc}(r)|^2]$ changes with time would separate static KPZ spatial fluctuations from dynamical noise.
  • For $N>2$, the counting argument suggests that the effective fluctuation exponent should deviate from pure $1/3$ even with strong random two-body interactions; small-system exact diagonalization with $N=4$ or $5$ on chains of length up to $L=16$ could test whether the correlated-disorder regime survives.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper studies two spinless fermions in a one-dimensional disordered chain with random potentials and random long-range interactions. Working in the Fock-space graph, the authors compute the sample-to-sample fluctuations of ln|psi_loc(r)|^2 for a fixed initial state and report a growth exponent beta ~ 1/2 when only random potentials are present and a crossover to beta ~ 1/3 when random long-range interactions dominate. The interpretation is based on a forward-scattering approximation that maps the Fock-space problem onto a (1+1)-dimensional directed polymer, and it is corroborated by a complex directed-polymer model with competing point and columnar disorder. The paper concludes that the structure of the disorder in Fock space—correlated columnar versus uncorrelated point—controls the universality class of the fluctuations.

Significance. If correct, the result would establish a clean example in a disordered quantum system where the correlation structure of Fock-space on-site energies determines whether wavefunction fluctuations follow a random-walk-like 1/2 exponent or the KPZ 1/3 exponent. The numerical effort is substantial, with up to 9620 disorder realizations for L=256, and the exact covariance relation in Eq. (18) is a useful, rigorous ingredient. The comparison between the TIP problem and a directed-polymer model with competing disorder is suggestive and potentially valuable. However, the central universality claim currently rests on a single exponent estimated by eye and on a mapping that is asserted rather than derived, so the significance is conditional on a more careful and quantitative validation.

major comments (3)
  1. [Section III A and Section V A] The mapping from the FSA path sum in Eq. (11) to the DP partition function in Eq. (12), and then to the Vp+Vc disorder model of Eq. (19), omits a realization-dependent common factor. In Eq. (11), every denominator is E_Q - E_{S_l}; rewriting T/(E_Q - E_{S_l}) = (T/E_Q)/(1 - E_{S_l}/E_Q) shows that all paths to distance r carry a common factor (T/E_Q)^r. Since E_Q = V_1 + V_L is random when WD=0, this factor contributes r ln|E_Q| to ln|psi_loc(r)|^2 and hence a contribution to sigma scaling as r, which would overwhelm the reported r^{1/2} or r^{1/3}. The simplified DP of Sec. V instead uses the bare on-site energies V_p(i,j)+V_c(i,j) with V_c(i,j)=V_i+V_j, and it uses V directly rather than the logarithmic disorder V_l = ln(E_Q - E_{S_l}) that actually enters Eq. (12). The exact covariance in Eq. (18) is for the bare E_S, not for the logarithm that appears in the DP weights. Please clarify whether E_Q in Eq. (11) is intended to be the eigenenergy E_X (a fixed ensemble parameter) or the random on-site energy of Q, and in either case provide a numerical test of the exact FSA path sum on the triangular Fock graph against the simplified Vp+Vc DP, including the contribution of the common factor.
  2. [Section IV A, Figs. 4-5] The claim that the crossover to beta ~ 1/3 places the TIP fluctuations in the (1+1)D KPZ universality class is supported only by a visual comparison of the slope of sigma[ln|psi_loc(r)|^2] with dashed lines r^{1/2} and r^{1/3}. There are no fits with quoted ranges or uncertainties, no finite-size scaling (all data shown are for L=256 and t=500), and no test of the distribution of ln|psi_loc(r)|^2. Since a single growth exponent does not uniquely identify a universality class, please add a quantitative determination of beta (for example, local logarithmic slopes with error bars over a fitted window), a check of stability with L, and preferably a distributional or scaling-collapse test before calling the class KPZ.
  3. [Section III B and Fig. 3] The use of a single time t=500 to define |psi_loc(r)|^2 is not fully justified. The IPR plateaus in Fig. 3 show that the total degree of localization is quasi-steady, but they do not imply that the sample-to-sample variance of ln|psi(r)|^2 at each distance r has converged, especially since persistent temporal fluctuations are acknowledged in Refs. [99,100]. Please show for at least the parameter sets of Figs. 4 and 5 that sigma[ln|psi(r)|^2] is stable when averaged over a time window after t>100, or provide a quantitative bound on the residual time dependence.
minor comments (3)
  1. [Section I] There is a typo in the phrase "disordered quantum ystems" in the introduction; it should read "disordered quantum systems."
  2. [Section V B] The sentence stating that "the fluctuation growth exponent of 1/3 emerges only under purely point disorder (gamma=1)" appears inconsistent with the preceding description of a crossover in Fig. 6 and with the TIP results at intermediate WV, WD. Please clarify whether the real DP requires gamma=1 while the complex DP crosses over at finite gamma, or whether the text should refer to the point-disorder-dominated regime rather than purely point disorder.
  3. [Fig. 5 caption] The caption says "red and black dashed lines indicate the algebraic behaviors r^{1/2} and r^{1/3}, respectively," but the main text describes the transition as from 1/3 to 1/2 with increasing alpha. Please make explicit in the caption which color corresponds to which exponent and how the panels should be read.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 1/2 and 1/3 exponents are measured in independent TIP and directed-polymer numerics, not constructed from inputs; the single self-citation [74] is not load-bearing.

full rationale

The paper's derivation chain is: (i) the FSA path sum (Eq. 11) is rewritten as a complex directed-polymer partition function (Eq. 12); (ii) the on-site energy covariance from Eq. (5) is computed (Eq. 18) and used to motivate a DP model with columnar plus point disorder (Eq. 19); (iii) exact TIP time evolution and independent DP transfer-matrix simulations are used to extract the fluctuation exponent beta. None of these steps defines the target exponent into the model. The exponents 1/2 and 1/3 are not fitted parameters: the TIP data are compared with algebraic r^{1/2} and r^{1/3} reference lines, while beta is extracted from the same data as a measured scaling exponent, so this is a benchmark test, not a forced fit. The Sec. V DP model is a separate numerical model whose disorder correlations are chosen to match Eq. (5); observing the same crossover in it is a consistency check, not a derivation of the TIP result from the TIP result. The only self-citation is Ref. [74], which supplies the expected KPZ value for 2D localized wave packets; the paper's own TIP and DP numerics independently reproduce this value, so the citation is not load-bearing. The skeptical concern about the common denominator E_Q in Eq. (11) -- the FSA weights are log(E_Q - E_S_l), not the bare energies used in Eq. (19) -- is a possible modeling approximation or validity issue, but it is not a circular reduction: the TIP simulation is still an independent calculation of the original Hamiltonian. No circular step is exhibited.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the forward scattering approximation, the mapping of the Fock-space graph to a directed polymer, and the assumption that t=500 captures the localized stationary regime. No new particles or free parameters are introduced; the disorder strengths and evolution time are model inputs. The main axioms are domain assumptions from the disordered-systems and directed-polymer literature, none of which are machine-checked.

assumptions (5)
  • domain assumption The forward scattering approximation gives the localized wavefunction amplitude as a sum over directed paths, Eq. (11).
    Sec. III A. Assumes strong disorder T/W << 1 and neglects paths with loops and longer excursions. Standard in the FSA literature [68-73] but not proven for this graph.
  • domain assumption Complex directed polymers with random phases share the fluctuation exponents of real directed polymers and belong to the KPZ universality class.
    Sec. III A and V A, cites [94-98]. Underpins interpreting ln|ψ|^2 as a DP free energy.
  • domain assumption The localized wavefunction's log-density has the form -2r/ξ + (r/ξ)^β Γ χ(r) + Λ, Eq. (14).
    Sec. III B. Adopted from prior work [74,101-105]; this is the basis for extracting β from σ[ln|ψ|^2].
  • domain assumption At t=500 the wavefunction is in the localized stationary regime, so sample-to-sample fluctuations at fixed time represent eigenstate fluctuations.
    Sec. III B, Fig. 3. IPR is stable for t>100, but temporal fluctuations are not quantitatively analyzed.
  • domain assumption The Fock-space TIP graph with the chosen point-to-point boundary condition maps to a (1+1)D directed polymer with point and columnar disorder.
    Sec. III A, Fig. 2, and Sec. V A. The static on-site energy covariance in Eq. (18) is exact, but the equivalence of the FSA path sum to the simplified DP model is not derived.

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Cite this review

Pith. "Pith review of Universal fluctuations of localized two interacting particles in one dimension." pith.science (2026). https://pith.science/paper/UZ75URVN

@misc{pith2026250201399,
  author       = {Pith},
  title        = {Pith review of: Universal fluctuations of localized two interacting particles in one dimension},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UZ75URVN}},
  note         = {Machine review of arXiv:2502.01399}
}
read the original abstract

We investigate the universal fluctuations of localized wavefunction in the Fock space of two interacting particles in one-dimensional disordered systems, focusing on the interplay between random potentials and random long-range interactions. By mapping the system onto a directed polymer problem, we show that random potentials alone produce correlated energies for the sites in the Fock space, giving rise to the fluctuation growth exponent 1/2. Introducing random long-range interactions alters these correlations and drives the system's fluctuations into the Kardar-Parisi-Zhang universality class in (1+1)D with the exponent 1/3. To validate the universality of the observed fluctuation scaling, we study a complex directed polymer model with competing point and columnar disorder. Our results confirm that columnar disorder corresponds to on-site energies in the Fock space from the random potentials, while point disorder models the effects of random long-range interactions between the two particles. These findings provide new insights into the Fock-space perspective for examining disordered quantum many-body systems, and emphasize the critical role of disorder structure in determining the universality class of fluctuations in localized quantum systems.

Figures

Figures reproduced from arXiv: 2502.01399 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of the Fock space for two spinless fermions [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. A directed polymer (DP) problem mapped from the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Disorder-averaged IPR as a function of time. (a) for cases with varying strengths of random potential and random [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Scaling of fluctuations [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Scaling of fluctuations [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Scaling of fluctuations in the free energy of real and [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

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Works this paper leans on

110 extracted references · 68 canonical work pages

  1. [1]

    P. W. Anderson, Absence of Diffusion in Certain Ran- dom Lattices, Phys. Rev.109, 1492 (1958)

    1958

  2. [2]

    Abrahams, P

    E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling Theory of Localiza- tion: AbsenceofQuantumDiffusioninTwoDimensions, Phys. Rev. Lett.42, 673 (1979)

    1979

  3. [3]

    Abrahams,50 years of Anderson Localization (World Scientific, Singapore, 2010)

    E. Abrahams,50 years of Anderson Localization (World Scientific, Singapore, 2010)

    2010

  4. [4]

    P. A. Lee and A. D. Stone, Universal Conductance Fluc- tuations in Metals, Phys. Rev. Lett.55, 1622 (1985)

    1985

  5. [5]

    P. A. Mello, Macroscopic approach to universal conduc- tance fluctuations in disordered metals, Phys. Rev. Lett. 60, 1089 (1988)

    1988

  6. [6]

    C. W. J. Beenakker, Random-matrix theory of quantum transport, Rev. Mod. Phys.69, 731 (1997)

    1997

  7. [7]

    A. D. Mirlin, Statistics of energy levels and eigenfunc- tions in disordered systems, Physics Reports326, 259 (2000)

    2000

  8. [8]

    P. A. Lee and T. V. Ramakrishnan, Disordered elec- tronic systems, Rev. Mod. Phys.57, 287 (1985)

    1985

Show all 110 references
  1. [9]

    Evers and A

    F. Evers and A. D. Mirlin, Anderson transitions, Rev. Mod. Phys.80, 1355 (2008)

    2008

  2. [10]

    Wegner, Inverse participation ratio in 2+ϵ dimen- sions, Zeitschrift für Physik B Condensed Matter36, 209 (1980)

    F. Wegner, Inverse participation ratio in 2+ϵ dimen- sions, Zeitschrift für Physik B Condensed Matter36, 209 (1980)

    1980

  3. [11]

    Castellani and L

    C. Castellani and L. Peliti, Multifractal wavefunction at the localisation threshold, Journal of Physics A: Math- ematical and General19, L429 (1986)

    1986

  4. [12]

    Feigel’man, L

    M. Feigel’man, L. Ioffe, V. Kravtsov, and E. Cuevas, Fractal superconductivity near localization threshold, Annals of Physics325, 1390 (2010)

    2010

  5. [13]

    Mott, Electrons in disordered structures, Advances in Physics16, 49 (1967)

    N. Mott, Electrons in disordered structures, Advances in Physics16, 49 (1967)

    1967

  6. [14]

    Fleishman and P

    L. Fleishman and P. W. Anderson, Interactions and the Anderson transition, Phys. Rev. B21, 2366 (1980)

    1980

  7. [15]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-body localiza- tion and thermalization in quantum statistical mechan- ics, Annual Review of Condensed Matter Physics6, 15 (2015)

    2015

  8. [16]

    D. A. Abanin and Z. Papic, Recent progress in many- body localization, Annalen der Physik 529, 1700169 (2017)

    2017

  9. [17]

    Alet and N

    F. Alet and N. Laflorencie, Many-body localization: An introduction and selected topics, Comptes Rendus. Physique 19, 498 (2018)

    2018

  10. [18]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Col- loquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys.91, 021001 (2019)

    2019

  11. [19]

    Sierant, M

    P. Sierant, M. Lewenstein, A. Scardicchio, L. Vidmar, and J. Zakrzewski, Many-Body Localization in the Age of Classical Computing (2024), arXiv:2403.07111 [cond- mat.dis-nn]

    2024 arXiv

  12. [20]

    I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Interact- ing Electrons in Disordered Wires: Anderson Localiza- tion and Low-T Transport, Phys. Rev. Lett.95, 206603 (2005)

    2005

  13. [21]

    Basko, I

    D. Basko, I. Aleiner, and B. Altshuler, Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states, Annals of Physics 321, 1126 (2006)

    2006

  14. [22]

    D. L. Shepelyansky, 3d Anderson transition for two elec- tronsin2d(1999),arXiv:cond-mat/9902246[cond-mat]. 11

    1999 arXiv

  15. [23]

    Romer, M

    R. Romer, M. Leadbeater, and M. Schreiber, Numerical results for two interacting particles in a random environ- ment, Annalen der Physik511, 675 (1999)

    1999

  16. [24]

    Ortuno and E

    M. Ortuno and E. Cuevas, Localized to extended states transition for two interacting particles in a two- dimensional random potential, Europhysics Letters46, 224 (1999)

    1999

  17. [25]

    D. L. Shepelyansky, Coherent Propagation of Two Inter- actingParticlesinaRandomPotential,PhysicalReview Letters 73, 2607 (1994)

    1994

  18. [26]

    Imry, Coherent Propagation of Two Interacting Par- ticles in a Random Potential, Europhysics Letters30, 405 (1995)

    Y. Imry, Coherent Propagation of Two Interacting Par- ticles in a Random Potential, Europhysics Letters30, 405 (1995)

    1995

  19. [27]

    Weinmann and J.-L

    D. Weinmann and J.-L. Pichard, Level Statistics and Localization for Two Interacting Particles in a Random Potential, Phys. Rev. Lett.77, 1556 (1996)

    1996

  20. [28]

    Frahm, A

    K. Frahm, A. Müller-Groeling, and J.-L. Pichard, Effec- tive σ model formulation for two interacting electrons in a disordered metal, Phys. Rev. Lett.76, 1509 (1996)

    1996

  21. [29]

    Frahm, A

    K. Frahm, A. Müller-Groeling, and J.-L. Pichard, Two interacting particles in a random potential: mapping onto one parameter localization theories without inter- action, Zeitschrift for Physik B Condensed Matter102, 261 (1997)

    1997

  22. [30]

    Waintal and J.-L

    X. Waintal and J.-L. Pichard, Two interacting particles in a disordered chain i: Multifractality of the interaction matrix elements, The European Physical Journal B - Condensed Matter and Complex Systems6, 117 (1998)

    1998

  23. [31]

    Waintal, D.Weinmann,andJ.-L

    X. Waintal, D.Weinmann,andJ.-L. Pichard, Twointer- acting particles in a disordered chain II: Critical statis- tics and maximum mixing of the one body states, The European Physical Journal B - Condensed Matter and Complex Systems7, 451 (1999)

    1999

  24. [32]

    De Toro Arias, X

    S. De Toro Arias, X. Waintal, and J.-L. Pichard, Two interacting particles in a disordered chain III: Dynam- ical aspects of the interplay disorder-interaction, The European Physical Journal B - Condensed Matter and Complex Systems10, 149 (1999)

    1999

  25. [33]

    Frahm, A

    K. Frahm, A. Müller-Groeling, J.-L. Pichard, and D. Weinmann, Scaling in Interaction-Assisted Coherent Transport, Europhysics Letters31, 169 (1995)

    1995

  26. [34]

    Borgonovi and D

    F. Borgonovi and D. L. Shepelyansky, Enhancement of localization length for two interacting kicked rotators, Nonlinearity 8, 877 (1995)

    1995

  27. [35]

    von Oppen, T

    F. von Oppen, T. Wettig, and J. Muller, Interaction- Induced Delocalization of Two Particles in a Random Potential: Scaling Properties, Physical Review Letters 76, 491 (1996)

    1996

  28. [36]

    R. A. Römer and M. Schreiber, No Enhancement of the Localization Length for Two Interacting Particles in a Random Potential, Phys. Rev. Lett.78, 515 (1997)

    1997

  29. [37]

    I. V. Ponomarev and P. G. Silvestrov, Coherent prop- agation of interacting particles in a random potential: The mechanism of enhancement, Physical Review B56, 3742 (1997)

    1997

  30. [38]

    D. O. Krimer, R. Khomeriki, and S. Flach, Two inter- acting particles in a random potential, JETP Letters 94, 406 (2011)

    2011

  31. [39]

    D. O. Krimer and S. Flach, Interaction-induced connec- tivity of disordered two-particle states, Phys. Rev. B91, 100201 (2015)

    2015

  32. [40]

    K. M. Frahm, Eigenfunction structure and scaling of two interacting particles in the one-dimensional Ander- son model, The European Physical Journal B89, 115 (2016)

    2016

  33. [41]

    Thongjaomayum, A

    D. Thongjaomayum, A. Andreanov, T. Engl, and S. Flach, Taming two interacting particles with disor- der, Physical Review B100, 224203 (2019)

    2019

  34. [42]

    N. Macé, F. Alet, and N. Laflorencie, Multifractal Scal- ings Across the Many-Body Localization Transition, Phys. Rev. Lett.123, 180601 (2019)

    2019

  35. [43]

    Roy and D

    S. Roy and D. E. Logan, Localization on Certain Graphs with Strongly Correlated Disorder, Phys. Rev. Lett. 125, 250402 (2020)

    2020

  36. [44]

    Tarzia, Many-body localization transition in Hilbert space, Phys

    M. Tarzia, Many-body localization transition in Hilbert space, Phys. Rev. B102, 014208 (2020)

    2020

  37. [45]

    Pietracaprina and N

    F. Pietracaprina and N. Laflorencie, Hilbert-space frag- mentation, multifractality, and many-body localization, Annals of Physics435, 168502 (2021), special Issue on Localisation 2020

    2021

  38. [46]

    Biroli, A

    G. Biroli, A. K. Hartmann, and M. Tarzia, Large- deviation analysis of rare resonances for the many- body localization transition, Phys. Rev. B110, 014205 (2024)

    2024

  39. [47]

    Scoquart, I

    T. Scoquart, I. V. Gornyi, and A. D. Mirlin, Role of fock-space correlations in many-body localization, Phys. Rev. B109, 214203 (2024)

    2024

  40. [48]

    Roy and D

    S. Roy and D. E. Logan, The Fock-space landscape of many-body localisation, Journal of Physics: Condensed Matter 37, 073003 (2024)

    2024

  41. [49]

    K. S. Tikhonov, A. D. Mirlin, and M. A. Skvortsov, Anderson localization and ergodicity on random regular graphs, Phys. Rev. B94, 220203 (2016)

    2016

  42. [50]

    García-Mata, O

    I. García-Mata, O. Giraud, B. Georgeot, J. Martin, R. Dubertrand, and G. Lemarié, Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality, Phys. Rev. Lett.118, 166801 (2017)

    2017

  43. [51]

    Welsh and D

    S. Welsh and D. E. Logan, Simple probability distribu- tions on a Fock-space lattice, Journal of Physics: Con- densed Matter30, 405601 (2018)

    2018

  44. [52]

    Semeghini, H

    G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kali- nowski, R. Samajdar, A. Omran, S. Sachdev, A. Vish- wanath, M. Greiner, V. Vuletic, and M. D. Lukin, Prob- ingtopologicalspinliquidsonaprogrammablequantum simulator, Sci...

    2021

  45. [53]

    K. J. S. et al., Realizing topologically ordered states on a quantum processor, Science374, 1237 (2021)

    2021

  46. [54]

    Schreiber, S

    M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I.Bloch,Observationofmany-bodylocalizationofinter- acting fermions in a quasirandom optical lattice, Science 349, 842 (2015)

    2015

  47. [55]

    yoon Choi, S

    J. yoon Choi, S. Hild, J. Zeiher, P. Schauß, A. Rubio- Abadal, T. Yefsah, V. Khemani, D. A. Huse, I. Bloch, and C. Gross, Exploring the many-body localization transition in two dimensions, Science352, 1547 (2016)

    2016

  48. [56]

    Blatt and C

    R. Blatt and C. F. Roos, Quantum simulations with trapped ions, Nature Physics8, 277 (2012)

    2012

  49. [57]

    Islam, C

    R. Islam, C. Senko, W. C. Campbell, S. Korenblit, J. Smith, A. Lee, E. E. Edwards, C.-C. J. Wang, J. K. Freericks, and C. Monroe, Emergence and Frustration of Magnetism with Variable-Range Interactions in a Quan- tum Simulator, Science340, 583 (2013)

    2013

  50. [58]

    Ritsch, P

    H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Cold atoms in cavity-generated dynamical optical po- tentials, Rev. Mod. Phys.85, 553 (2013). 12

    2013

  51. [59]

    Endres, H

    M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, Atom-by-atom assembly of defect-free one-dimensional cold atom arrays, Science 354, 1024 (2016)

    2016

  52. [60]

    Labuhn, D

    H. Labuhn, D. Barredo, S. Ravets, S. de Leseleuc, T. Macri, T. Lahaye, and A. Browaeys, Tunable two- dimensional arrays of single Rydberg atoms for realizing quantum Ising models, Nature534, 667 (2016)

    2016

  53. [61]

    Zeiher, J.-y

    J. Zeiher, J.-y. Choi, A. Rubio-Abadal, T. Pohl, R. van Bijnen, I. Bloch, and C. Gross, Coherent Many-Body Spin Dynamics in a Long-Range Interacting Ising Chain, Phys. Rev. X7, 041063 (2017)

    2017

  54. [62]

    T. D. Farokh Mivehvar, Francesco Piazza and H. Ritsch, Cavity qed with quantum gases: new paradigms in many-body physics, Advances in Physics70, 1 (2021)

    2021

  55. [63]

    Monroe, W

    C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Programmable quantum simulations of spin sys- tems with trapped ions, Rev. Mod. Phys.93, 025001 (2021)

    2021

  56. [64]

    Hollerith, K

    S. Hollerith, K. Srakaew, D. Wei, A. Rubio-Abadal, D. Adler, P. Weckesser, A. Kruckenhauser, V. Walther, R. van Bijnen, J. Rui, C. Gross, I. Bloch, and J. Zeiher, Realizing Distance-Selective Interactions in a Rydberg- Dressed Atom Array, Phys. Rev. Lett. 128, 113602 (2022)

    2022

  57. [65]

    Defenu, T

    N. Defenu, T. Donner, T. Macrì, G. Pagano, S. Ruffo, and A. Trombettoni, Long-range interacting quantum systems, Rev. Mod. Phys.95, 035002 (2023)

    2023

  58. [66]

    Randall, C

    J. Randall, C. E. Bradley, F. V. van der Gron- den, A. Galicia, M. H. Abobeih, M. Markham, D. J. Twitchen, F. Machado, N. Y. Yao, and T. H. Taminiau, Many-body localized discrete time crystal with a pro- grammable spin-based quantum simulator, Science374, 1474 (2021)

    2021

  59. [67]

    Mi and et

    X. Mi and et. al., Time-crystalline eigenstate order on a quantum processor, Nature601, 531 (2022)

    2022

  60. [68]

    E. A. Stern, Forward-Scattering Approximation for Dis- ordered Systems, Phys. Rev. B7, 1303 (1973)

    1973

  61. [69]

    Nguen, B

    V. Nguen, B. Spivak, and B. Shkovskii, Tunnel hop- ping in disordered systems, Zh. Eksp. Teor. Fiz89, 1770 (1985)

    1985

  62. [70]

    Medina and M

    E. Medina and M. Kardar, Quantum interference effects for strongly localized electrons, Phys. Rev. B46, 9984 (1992)

    1992

  63. [71]

    V. Ros, M. MÃŒller, and A. Scardicchio, Integrals of motion in the many-body localized phase, Nuclear Physics B891, 420 (2015)

    2015

  64. [72]

    Pietracaprina, V

    F. Pietracaprina, V. Ros, and A. Scardicchio, Forward approximation as a mean-field approximation for the Andersonandmany-bodylocalizationtransitions,Phys. Rev. B93, 054201 (2016)

    2016

  65. [73]

    C. L. Baldwin, C. R. Laumann, A. Pal, and A. Scardic- chio, Clustering of nonergodic eigenstates in quantum spin glasses, Phys. Rev. Lett.118, 127201 (2017)

    2017

  66. [74]

    S. Mu, J. Gong, and G. Lemarié, Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two- Dimensional Wave Packets, Phys. Rev. Lett. 132, 046301 (2024)

    2024

  67. [75]

    Kardar, G

    M. Kardar, G. Parisi, and Y.-C. Zhang, Dynamic Scal- ing of Growing Interfaces, Phys. Rev. Lett. 56, 889 (1986)

    1986

  68. [76]

    Corwin, The Kardar-Parisi-Zhang equation and uni- versality class, Random Matrices: Theory and Applica- tions 01, 1130001 (2012)

    I. Corwin, The Kardar-Parisi-Zhang equation and uni- versality class, Random Matrices: Theory and Applica- tions 01, 1130001 (2012)

    2012

  69. [77]

    Halpin-Healy and K

    T. Halpin-Healy and K. A. Takeuchi, A kpz cocktail- shaken, not stirred..., Journal of Statistical Physics160, 794 (2015)

    2015

  70. [78]

    K. A. Takeuchi, An appetizer to modern developments on the Kardar-Parisi-Zhang universality class, Physica A: Statistical Mechanics and its Applications504, 77 (2018)

    2018

  71. [79]

    Spohn, The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises, Journal of Statistical Mechan- ics: Theory and Experiment2020, 044001 (2020)

    H. Spohn, The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises, Journal of Statistical Mechan- ics: Theory and Experiment2020, 044001 (2020)

    2020

  72. [80]

    Kardar and Y.-C

    M. Kardar and Y.-C. Zhang, Scaling of Directed Poly- mers in Random Media, Phys. Rev. Lett. 58, 2087 (1987)

    1987

  73. [81]

    Mézard, On the glassy nature of random directed polymers in two dimensions, Journal de Physique51, 1831 (1990)

    M. Mézard, On the glassy nature of random directed polymers in two dimensions, Journal de Physique51, 1831 (1990)

    1990

  74. [82]

    Halpin-Healy and Y.-C

    T. Halpin-Healy and Y.-C. Zhang, Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechan- ics, Physics Reports254, 215 (1995)

    1995

  75. [83]

    Calabrese, P

    P. Calabrese, P. Le Doussal, and A. Rosso, Free-energy distribution of the directed polymer at high tempera- ture, Europhysics Letters90, 20002 (2010)

    2010

  76. [84]

    Dotsenko, Bethe ansatz derivation of the Tracy- Widom distribution for one-dimensional directed poly- mers, Europhysics Letters90, 20003 (2010)

    V. Dotsenko, Bethe ansatz derivation of the Tracy- Widom distribution for one-dimensional directed poly- mers, Europhysics Letters90, 20003 (2010)

    2010

  77. [85]

    A. K. Hartmann, A. Krajenbrink, and P. Le Dous- sal, Probing large deviations of the Kardar-Parisi-Zhang equation at short times with an importance sampling of directed polymers in random media, Phys. Rev. E101, 012134 (2020)

    2020

  78. [86]

    Tang and I

    L.-H. Tang and I. F. Lyuksyutov, Directed polymer lo- calization in a disordered medium, Phys. Rev. Lett.71, 2745 (1993)

    1993

  79. [87]

    Balents and M

    L. Balents and M. Kardar, Delocalization of Flux Lines from Extended Defects by Bulk Randomness, Euro- physics Letters23, 503 (1993)

    1993

  80. [88]

    Arsenin, T

    I. Arsenin, T. Halpin-Healy, and J. Krug, Competing effects of point versus columnar defects on the roughen- ing of directed polymers in random media, Phys. Rev. E 49, R3561 (1994)

    1994

  81. [89]

    Kardar, Domain walls subject to quenched impu- rities (invited), Journal of Applied Physics 61, 3601 (1987)

    M. Kardar, Domain walls subject to quenched impu- rities (invited), Journal of Applied Physics 61, 3601 (1987)

    1987

  82. [91]

    Chu and M

    S. Chu and M. Kardar, Probability distributions for di- rected polymers in random media with correlated noise, Phys. Rev. E94, 010101 (2016)

    2016

  83. [92]

    Zhang, Directed Polymers with Complex Ampli- tudes, Phys

    Y.-C. Zhang, Directed Polymers with Complex Ampli- tudes, Phys. Rev. Lett.62, 979 (1989)

    1989

  84. [93]

    Zhang, Directed Polymers with Complex Ampli- tudes, Europhysics Letters9, 113 (1989)

    Y.-C. Zhang, Directed Polymers with Complex Ampli- tudes, Europhysics Letters9, 113 (1989)

    1989

  85. [94]

    Medina, M

    E. Medina, M. Kardar, Y. Shapir, and X. R. Wang, Interference of Directed Paths in Disordered Systems, Phys. Rev. Lett.62, 941 (1989)

    1989

  86. [95]

    M. P. Gelfand, Random walks in random media with random signs, Physica A: Statistical Mechanics and its Applications 177, 67 (1991). 13

    1991

  87. [96]

    Blum and Y

    T. Blum and Y. Y. Goldschmidt, Directed paths with random phases, Nuclear Physics B380, 588 (1992)

    1992

  88. [97]

    Roux and A

    S. Roux and A. Coniglio, Interference of directed paths, Journal of Physics A: Mathematical and General27, 5467 (1994)

    1994

  89. [98]

    Gangopadhyay, V

    A. Gangopadhyay, V. Galitski, and M. Müller, Magne- toresistance of an Anderson Insulator of Bosons, Phys. Rev. Lett.111, 026801 (2013)

    2013

  90. [99]

    Ziraldo, A

    S. Ziraldo, A. Silva, and G. E. Santoro, Relaxation Dy- namics of Disordered Spin Chains: Localization and the Existence of a Stationary State, Phys. Rev. Lett.109, 247205 (2012)

    2012

  91. [100]

    Ziraldo and G

    S. Ziraldo and G. E. Santoro, Relaxation and thermal- ization after a quantum quench: Why localization is important, Phys. Rev. B87, 064201 (2013)

    2013

  92. [101]

    D. S. Fisher and D. A. Huse, Directed paths in a random potential, Phys. Rev. B43, 10728 (1991)

    1991

  93. [102]

    K. A. Takeuchi, M. Sano, T. Sasamoto, and H. Spohn, Growing interfaces uncover universal fluctuations be- hind scale invariance, Scientific Reports1, 34 (2011)

    2011

  94. [103]

    Monthus and T

    C. Monthus and T. Garel, Random Transverse Field Ising Model in dimension d>1: scaling analysis in the disordered phase from the Directed Polymer model, Journal of Physics A: Mathematical and Theoretical45, 095002 (2012)

    2012

  95. [104]

    A. M. Somoza, M. Ortuño, and J. Prior, Universal Dis- tribution Functions in Two-Dimensional Localized Sys- tems, Phys. Rev. Lett.99, 116602 (2007)

    2007

  96. [105]

    Lemarié, Glassy Properties of Anderson Localiza- tion: Pinning, Avalanches, and Chaos, Phys

    G. Lemarié, Glassy Properties of Anderson Localiza- tion: Pinning, Avalanches, and Chaos, Phys. Rev. Lett. 122, 030401 (2019)

    2019

  97. [106]

    Civale, A

    L. Civale, A. D. Marwick, T. K. Worthington, M. A. Kirk, J. R. Thompson, L. Krusin-Elbaum, Y. Sun, J. R. Clem, and F. Holtzberg, Vortex confinement by colum- nar defects inyba2cu3o7 crystals: Enhanced pinning at high fields and temperatures, Phys. Rev. Lett.67, 648 (1991)

    1991

  98. [107]

    T. Hwa, P. Le Doussal, D. R. Nelson, and V. M. Vi- nokur, Flux pinning and forced vortex entanglement by splayed columnar defects, Phys. Rev. Lett.71, 3545 (1993)

    1993

  99. [108]

    D. R. Nelson and V. M. Vinokur, Boson localization and correlated pinning of superconducting vortex ar- rays, Phys. Rev. B48, 13060 (1993)

    1993

  100. [109]

    Giamarchi and P

    T. Giamarchi and P. Le Doussal, Variational theory of elastic manifolds with correlated disorder and localiza- tion of interacting quantum particles, Phys. Rev. B53, 15206 (1996)

    1996

  101. [110]

    Forster, D

    D. Forster, D. R. Nelson, and M. J. Stephen, Large- distance and long-time properties of a randomly stirred fluid, Phys. Rev. A16, 732 (1977)

    1977

  102. [111]

    Medina, T

    E. Medina, T. Hwa, M. Kardar, and Y.-C. Zhang, Burg- ers equation with correlated noise: Renormalization- group analysis and applications to directed polymers and interface growth, Phys. Rev. A39, 3053 (1989)

    1989

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