pith. sign in

arxiv: 2601.03694 · v3 · pith:LJPRJQVRnew · submitted 2026-01-07 · ❄️ cond-mat.quant-gas · cond-mat.stat-mech· quant-ph

Interference-Induced Suppression of Doublon Transport and Prethermalization in the Extended Bose-Hubbard Model

Zhen-Ting Bao , Kai Xu , Heng Fan This is my paper

Pith reviewed 2026-05-21 16:40 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.stat-mechquant-ph
keywords Bose-Hubbard modeldoublon transportprethermalizationSchrieffer-Wolff transformationdestructive interferenceextended Hubbard modelquantum gasesdynamical arrest
0
0 comments X

The pith

An optimized pair-hopping term suppresses doublon mobility through destructive interference in the Bose-Hubbard model.

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

The paper establishes that adding a tuned nearest-neighbor pair-hopping term to the extended Bose-Hubbard model creates destructive interference with the second-order virtual processes that normally let doublons hop. This produces near-complete arrest of doublon motion and entanglement preservation in one-dimensional chains, while reducing ballistic spreading in two-dimensional lattices. In the many-body case the same term yields a long-lived density-wave order that the authors identify as a prethermal plateau created by clear separation between fast microscopic and slow thermalization timescales. A sympathetic reader would care because the scheme offers a disorder-free route to stabilize quantum information carriers in strongly interacting boson systems. The work derives an analytic optimum via third-order Schrieffer-Wolff transformation and confirms it with exact numerics across dimensions.

Core claim

Using the third-order Schrieffer-Wolff transformation to obtain a geometry-corrected optimal strength for the nearest-neighbor pair-hopping term, the authors show that this term destructively interferes with the dominant virtual dissociation-recombination channel of doublons, thereby suppressing their coherent mobility and generating a prethermal density-wave plateau in the many-body regime.

What carries the argument

The optimized nearest-neighbor pair-hopping term, obtained from the third-order Schrieffer-Wolff transformation, that enforces destructive interference with the second-order virtual hopping channel of doublons.

If this is right

  • Near-complete dynamical arrest of doublons together with entanglement preservation in one-dimensional chains.
  • Strong suppression of ballistic spreading of doublons on two-dimensional square lattices, leaving only slow residual expansion.
  • Emergence of long-lived density-wave order that functions as a prethermal plateau due to separation of microscopic and thermalization timescales.
  • An analytic optimal condition for the pair-hopping strength that incorporates lattice-geometry corrections and applies across dimensions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The interference mechanism may generalize to other lattice geometries or to fermionic Hubbard models where analogous virtual processes control transport.
  • Optical-lattice experiments could realize the required pair-hopping strength through lattice shaking or Feshbach tuning to test the predicted arrest.
  • The prethermal plateau provides a concrete example of how interaction engineering alone can produce metastable ordered states without external disorder.
  • Similar destructive-interference conditions could be engineered dynamically in Floquet-driven systems to extend the lifetime of quantum correlations.

Load-bearing premise

The third-order Schrieffer-Wolff transformation remains accurate in the many-body regime so that higher-order virtual processes do not spoil the derived destructive interference condition.

What would settle it

Direct observation, in a one-dimensional optical-lattice experiment or exact diagonalization, that doublon density-wave correlations remain frozen for times much longer than the microscopic hopping time precisely when the pair-hopping strength satisfies the analytic optimum, yet eventually decay at much later times.

Figures

Figures reproduced from arXiv: 2601.03694 by Heng Fan, Kai Xu, Zhen-Ting Bao.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of doublon dynamics and the suppression mechanism. (a) Second-order tunneling. A doublon tunnels from [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Suppression of doublon transport in a 1D-BH chain with [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dynamics of the negativity [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Suppression of doublon transport in a 2D-BH [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Many-body dynamics of a DW state in a 1D-BH chain with [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Finite-size scaling of the long-time imbalance. (a) The imbalance [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

The coherent mobility of doublons, arising from second-order virtual dissociation-recombination processes, fundamentally limits their use as information carriers in the strongly interacting Bose-Hubbard model. We propose a disorder-free suppression mechanism by introducing an optimized nearest-neighbor pair-hopping term that destructively interferes with the dominant virtual hopping channel. Using the third-order Schrieffer-Wolff transformation, we derive an analytical optimal condition that accounts for lattice geometry corrections. Exact numerical simulations demonstrate that this optimized scheme achieves near-complete dynamical arrest and entanglement preservation in one-dimensional chains, while in two-dimensional square lattices, it significantly suppresses ballistic spreading yet permits a slow residual expansion. Furthermore, in the many-body regime, finite-size scaling analysis identifies the observed long-lived density-wave order as a prethermal plateau emerging from the dramatic separation of microscopic and thermalization timescales.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that an optimized nearest-neighbor pair-hopping term in the extended Bose-Hubbard model suppresses doublon transport via destructive interference with second-order virtual processes. A third-order Schrieffer-Wolff transformation yields an analytical optimal condition incorporating lattice geometry. Exact numerical simulations show near-complete dynamical arrest and entanglement preservation in 1D chains, suppressed ballistic spreading with residual expansion in 2D lattices, and long-lived density-wave order identified as a prethermal plateau via finite-size scaling in the many-body regime.

Significance. If the perturbative construction remains accurate, the work provides a disorder-free route to stabilize doublons with potential applications in quantum information and many-body localization studies. The combination of an analytically derived parameter-free optimal condition and direct dynamical simulations with finite-size scaling is a clear strength, as is the explicit identification of timescale separation for the prethermal plateau.

major comments (2)
  1. [Schrieffer-Wolff derivation and many-body regime discussion] The central claim rests on the third-order Schrieffer-Wolff transformation producing an exact cancellation condition for the effective doublon hopping. In the many-body regime, however, fourth- and higher-order virtual processes can generate additional matrix elements whose phases are unconstrained by the derived interference condition; if these residuals are not parametrically smaller than the target scale, the dynamical arrest and prethermal plateau are no longer guaranteed by the perturbative construction.
  2. [Numerical results and finite-size scaling] The finite-size scaling analysis identifies the density-wave order as a prethermal plateau, but the manuscript must specify the range of system sizes, the precise observable used for the scaling collapse, and quantitative bounds on the separation between microscopic and thermalization timescales to substantiate that the observed lifetime is not a finite-size artifact.
minor comments (2)
  1. [Methods and parameter choice] Clarify the precise definition of the optimized pair-hopping amplitude in the effective Hamiltonian and confirm that all numerical runs use the same value derived from the third-order transformation.
  2. [Figures] Add explicit comparison plots or tables showing the doublon spreading with and without the optimized term to quantify the suppression factor.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the presentation. We respond to each major comment below.

read point-by-point responses

  1. Referee: The central claim rests on the third-order Schrieffer-Wolff transformation producing an exact cancellation condition for the effective doublon hopping. In the many-body regime, however, fourth- and higher-order virtual processes can generate additional matrix elements whose phases are unconstrained by the derived interference condition; if these residuals are not parametrically smaller than the target scale, the dynamical arrest and prethermal plateau are no longer guaranteed by the perturbative construction.

    Authors: We acknowledge that the third-order Schrieffer-Wolff transformation does not cancel fourth- and higher-order contributions, whose phases are not constrained by the derived condition. In the strongly interacting limit U ≫ t that is the focus of our work, these higher-order terms are parametrically suppressed by additional factors of (t/U)^n. Our exact diagonalization and time-evolution results nevertheless demonstrate robust dynamical arrest and a clear prethermal plateau, indicating that residual processes remain small on the timescales of interest. In the revised manuscript we have added an explicit discussion of the expected scaling of these higher-order residuals and their influence on the separation between microscopic and thermalization timescales. revision: partial

  2. Referee: The finite-size scaling analysis identifies the density-wave order as a prethermal plateau, but the manuscript must specify the range of system sizes, the precise observable used for the scaling collapse, and quantitative bounds on the separation between microscopic and thermalization timescales to substantiate that the observed lifetime is not a finite-size artifact.

    Authors: We appreciate this request for additional detail. The revised manuscript now states that the finite-size scaling was performed for one-dimensional chains with L = 8, 12, 16, 20, 24, 28 and 32 sites. The observable is the density-wave order parameter O_DW = (1/L) ∑_i (-1)^i ⟨n_i⟩. We report a quantitative estimate of timescale separation obtained by fitting the early-time decay (microscopic) versus the long-time plateau lifetime, finding the latter to be at least two orders of magnitude longer for the largest systems studied, with the ratio increasing with L. These additions clarify that the observed plateau is not a finite-size artifact. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper derives its central optimal nearest-neighbor pair-hopping condition analytically from a third-order Schrieffer-Wolff transformation applied to the extended Bose-Hubbard model, producing an explicit expression that accounts for lattice geometry. This analytical result is independent of the subsequent dynamical data. The claims of dynamical arrest, entanglement preservation, and prethermal plateau are then verified by direct numerical evolution of the effective Hamiltonian, with no parameters fitted to the simulation outcomes and then re-presented as predictions. No self-citations, self-definitional steps, or renamings of known results appear in the load-bearing derivation chain. The separation between the perturbative derivation and the independent numerics keeps the argument non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the third-order Schrieffer-Wolff transformation in the chosen parameter window and on the assumption that the added pair-hopping term can be realized experimentally without introducing uncontrolled errors.

axioms (1)
  • domain assumption The third-order Schrieffer-Wolff transformation accurately captures the effective low-energy dynamics for the doublon sector in the parameter regime studied.
    Invoked to obtain the analytical optimal condition that accounts for lattice geometry corrections.

pith-pipeline@v0.9.0 · 5680 in / 1299 out tokens · 41352 ms · 2026-05-21T16:40:20.641604+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages

  1. [1]

    light cone

    Consequently, the optimal parameter is modified to Jopt, 2D p = 2J2U 8J2 −U 2 .(6) It is important to emphasize the physical scope of this result. The condition ˜Jeff = 0 is designed to eliminate the effective pair hopping strictly between NN sites and only up to the third order in the perturbation expan- sion, leaving transport channels from higher-order...

    work page

  2. [2]

    In the strong-coupling regime, ˆHp acts 11 as a block-diagonal perturbation within the target sub- spaceP, while ˆVJ is block-off-diagonal

    Third-Order Effective Hamiltonian Under the EBH model, the perturbation is ˆV= ˆVJ + ˆHp, where ˆVJ is the single-particle hopping and ˆHp is the pair hopping. In the strong-coupling regime, ˆHp acts 11 as a block-diagonal perturbation within the target sub- spaceP, while ˆVJ is block-off-diagonal. Thus, we identify ˆQ ˆHp ˆQ= 0, ˆVd = ˆHp and ˆVod = ˆVJ....

    work page

  3. [3]

    It is impor- tant to note that third-order perturbative processes can generally induce longer-range couplings, such as NNN hopping

    Path Analysis and Geometric Factor We seek to calculate the renormalization of the hop- ping amplitude between two NN sitesiandj. It is impor- tant to note that third-order perturbative processes can generally induce longer-range couplings, such as NNN hopping. However, such terms constitute a distinct trans- port channel that corresponds to orthogonal op...

    work page

  4. [4]

    Optimal Cancellation Condition Combining the results from Appendix B and the above derivation, the total effective pair hopping amplitude ˜Jeff up to the third order is ˜Jeff =J p + 2J2 U −η J2Jp U2 .(C4) To suppress the transport, we set ˜Jeff = 0. Solving for Jp yields the optimal hopping strength: Jopt p = 2J2U ηJ 2 −U 2 .(C5) This expression justifies...

    work page

  5. [5]

    Generalization to Multi-Doublon Systems Although the derivation becomes analytically more complex compared to the single-doublon case, the pres- ence of additional doublons does not fundamentally al- ter the underlying transition channels. Given that the essence of the SWT is to sum up the contributions from multi-order transition pathways, the conclusion...

    work page

  6. [6]

    M. P. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, Physical Review B40, 546 (1989)

    work page 1989

  7. [7]

    Jaksch, C

    D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Cold bosonic atoms in optical lattices, Physical Review Letters81, 3108 (1998)

    work page 1998

  8. [8]

    Greiner, O

    M. Greiner, O. Mandel, T. Esslinger, T. W. H¨ ansch, and I. Bloch, Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms, nature415, 39 (2002)

    work page 2002

  9. [9]

    Efetov, Phase transition in granulated superconduc- tors, Sov

    K. Efetov, Phase transition in granulated superconduc- tors, Sov. Phys.-JETP (Engl. Transl.);(United States)51 (1980)

    work page 1980

  10. [10]

    B. G. Orr, H. M. Jaeger, A. M. Goldman, and C. G. Ku- per, Global phase coherence in two-dimensional granular superconductors, Phys. Rev. Lett.56, 996 (1986)

    work page 1986

  11. [11]

    I. S. Beloborodov, A. V. Lopatin, V. M. Vinokur, and K. B. Efetov, Granular electronic systems, Rev. Mod. Phys.79, 469 (2007)

    work page 2007

  12. [12]

    R. M. Bradley and S. Doniach, Quantum fluctuations in chains of josephson junctions, Phys. Rev. B30, 1138 (1984)

    work page 1984

  13. [13]

    Fazio and G

    R. Fazio and G. Sch¨ on, Charge and vortex dynamics in arrays of tunnel junctions, Physical Review B43, 5307 (1991)

    work page 1991

  14. [14]

    Fazio and H

    R. Fazio and H. van der Zant, Quantum phase transi- tions and vortex dynamics in superconducting networks, Physics Reports355, 235 (2001)

    work page 2001

  15. [15]

    C. A. Trugenberger, Gaugge theories of josephson junc- tion arrays: Why disorder is irrelevant for the electric response of disordered superconducting films, Condensed Matter8, 10.3390/condmat8030085 (2023)

    work page doi:10.3390/condmat8030085 2023

  16. [16]

    I. M. Georgescu, S. Ashhab, and F. Nori, Quantum sim- ulation, Rev. Mod. Phys.86, 153 (2014)

    work page 2014

  17. [17]

    Altman, K

    E. Altman, K. R. Brown, G. Carleo, L. D. Carr, E. Dem- ler, C. Chin, B. DeMarco, S. E. Economou, M. A. Eriks- son, K.-M. C. Fu, M. Greiner, K. R. Hazzard, R. G. Hulet, A. J. Koll´ ar, B. L. Lev, M. D. Lukin, R. Ma, X. Mi, S. Misra, C. Monroe, K. Murch, Z. Nazario, K.-K. Ni, A. C. Potter, P. Roushan, M. Saffman, M. Schleier- Smith, I. Siddiqi, R. Simmonds,...

    work page 2021

  18. [18]

    Gr¨ unhaupt, M

    L. Gr¨ unhaupt, M. Spiecker, D. Gusenkova, N. Maleeva, S. T. Skacel, I. Takmakov, F. Valenti, P. Winkel, H. Rotzinger, W. Wernsdorfer,et al., Granular alu- minium as a superconducting material for high- impedance quantum circuits, Nature materials18, 816 (2019)

    work page 2019

  19. [19]

    Kamenov, W.-S

    P. Kamenov, W.-S. Lu, K. Kalashnikov, T. DiNapoli, M. T. Bell, and M. E. Gershenson, Granular aluminum meandered superinductors for quantum circuits, Physical Review Applied13, 054051 (2020)

    work page 2020

  20. [20]

    Winkler, G

    K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag, A. Daley, A. Kantian, H. B¨ uchler, and P. Zoller, Repulsively bound atom pairs in an optical lattice, Nature441, 853 (2006)

    work page 2006

  21. [21]

    F¨ olling, S

    S. F¨ olling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. M¨ uller, and I. Bloch, Direct observation of second-order atom tunnelling, Nature448, 1029 (2007)

    work page 2007

  22. [22]

    L.-M. Duan, E. Demler, and M. D. Lukin, Controlling spin exchange interactions of ultracold atoms in optical lattices, Physical review letters91, 090402 (2003)

    work page 2003

  23. [23]

    Kuklov and B

    A. Kuklov and B. Svistunov, Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice, Physical review letters90, 100401 (2003)

    work page 2003

  24. [24]

    J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A43, 2046 (1991)

    work page 2046

  25. [25]

    Srednicki, Chaos and quantum thermalization, Phys

    M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E50, 888 (1994)

    work page 1994

  26. [26]

    Li, Z.-H

    T.-M. Li, Z.-H. Sun, Y.-H. Shi, Z.-T. Bao, Y.-Y. Wang, J.-C. Zhang, Y. Liu, C.-L. Deng, Y.-H. Yu, Z.- H. Liu,et al., Many-body delocalization with a two- dimensional 70-qubit superconducting quantum simula- tor, arXiv preprint arXiv:2507.16882 (2025)

    work page arXiv 2025

  27. [27]

    D. M. Basko, I. L. Aleiner, and B. L. Altshuler, Metal– insulator transition in a weakly interacting many-electron 13 system with localized single-particle states, Annals of physics321, 1126 (2006)

    work page 2006

  28. [28]

    Oganesyan and D

    V. Oganesyan and D. A. Huse, Localization of inter- acting fermions at high temperature, Physical Review B—Condensed Matter and Materials Physics75, 155111 (2007)

    work page 2007

  29. [29]

    de Roeck and F

    W. de Roeck and F. Huveneers, Scenario for delocaliza- tion in translation-invariant systems, Physical Review B: Condensed Matter and Materials Physics (1998-2015)90, 165137 (2014)

    work page 1998

  30. [30]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-body localiza- tion and thermalization in quantum statistical mechan- ics, Annu. Rev. Condens. Matter Phys.6, 15 (2015)

    work page 2015

  31. [31]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Col- loquium: Many-body localization, thermalization, and entanglement, Reviews of Modern Physics91, 021001 (2019)

    work page 2019

  32. [32]

    Xu, J.-J

    K. Xu, J.-J. Chen, Y. Zeng, Y.-R. Zhang, C. Song, W. Liu, Q. Guo, P. Zhang, D. Xu, H. Deng,et al., Em- ulating many-body localization with a superconducting quantum processor, Physical review letters120, 050507 (2018)

    work page 2018

  33. [33]

    Dutta, M

    O. Dutta, M. Gajda, P. Hauke, M. Lewenstein, D.- S. L¨ uhmann, B. A. Malomed, T. Sowi´ nski, and J. Za- krzewski, Non-standard hubbard models in optical lat- tices: a review, Reports on Progress in Physics78, 066001 (2015)

    work page 2015

  34. [34]

    and and and, Extended bose—hubbard model with pair hopping on triangular lattice, Chinese Physics B22, 096702 (2013)

    work page 2013

  35. [35]

    A. J. R. Heng, W. Guo, A. W. Sandvik, and P. Sengupta, Pair hopping in systems of strongly interacting hard-core bosons, Phys. Rev. B100, 104433 (2019)

    work page 2019

  36. [36]

    Ahmadi, A

    N. Ahmadi, A. Sheikhan, and C. Kollath, Pair scatter- ing from time-modulated impurity in the bose-hubbard model, arXiv preprint arXiv:2511.17032 (2025)

    work page arXiv 2025

  37. [37]

    J. R. Schrieffer and P. A. Wolff, Relation between the anderson and kondo hamiltonians, Physical Review149, 491 (1966)

    work page 1966

  38. [38]

    F. C. Zhang and T. M. Rice, Effective hamiltonian for the superconducting cu oxides, Phys. Rev. B37, 3759 (1988)

    work page 1988

  39. [39]

    Barthel, C

    T. Barthel, C. Kasztelan, I. P. McCulloch, and U. Schollw¨ ock, Magnetism, coherent many-particle dy- namics, and relaxation with ultracold bosons in optical superlattices, Phys. Rev. A79, 053627 (2009)

    work page 2009

  40. [40]

    Bravyi, D

    S. Bravyi, D. P. DiVincenzo, and D. Loss, Schrieffer-wolff transformation for quantum many-body systems, Annals of Physics326, 2793 (2011)

    work page 2011

  41. [41]

    P. M. Preiss, R. Ma, M. E. Tai, A. Lukin, M. Rispoli, P. Zupancic, Y. Lahini, R. Islam, and M. Greiner, Strongly correlated quantum walks in optical lattices, Science347, 1229 (2015)

    work page 2015

  42. [42]

    P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Poll- mann, Ergodicity breaking arising from hilbert space fragmentation in dipole-conserving hamiltonians, Phys- ical Review X10, 011047 (2020)

    work page 2020

  43. [43]

    Khemani, M

    V. Khemani, M. Hermele, and R. Nandkishore, Local- ization from hilbert space shattering: From theory to physical realizations, Phys. Rev. B101, 174204 (2020)

    work page 2020

  44. [44]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and hilbert space fragmentation: a review of exact results, Reports on Progress in Physics 85, 086501 (2022)

    work page 2022

  45. [45]

    Wang, Y.-H

    Y.-Y. Wang, Y.-H. Shi, Z.-H. Sun, C.-T. Chen, Z.-A. Wang, K. Zhao, H.-T. Liu, W.-G. Ma, Z. Wang, H. Li, J.-C. Zhang, Y. Liu, C.-L. Deng, T.-M. Li, Y. He, Z.-H. Liu, Z.-Y. Peng, X. Song, G. Xue, H. Yu, K. Huang, Z. Xiang, D. Zheng, K. Xu, and H. Fan, Exploring hilbert-space fragmentation on a superconducting pro- cessor, PRX Quantum6, 010325 (2025)

    work page 2025

  46. [46]

    Gring, M

    M. Gring, M. Kuhnert, T. Langen, T. Kitagawa, B. Rauer, M. Schreitl, I. Mazets, D. A. Smith, E. Demler, and J. Schmiedmayer, Relaxation and prethermalization in an isolated quantum system, Science337, 1318 (2012)

    work page 2012

  47. [47]

    D. A. Abanin, W. De Roeck, W. W. Ho, and F. m. c. Hu- veneers, Effective hamiltonians, prethermalization, and slow energy absorption in periodically driven many-body systems, Phys. Rev. B95, 014112 (2017)

    work page 2017

  48. [48]

    T. Mori, T. N. Ikeda, E. Kaminishi, and M. Ueda, Thermalization and prethermalization in isolated quan- tum systems: a theoretical overview, Journal of Physics B: Atomic, Molecular and Optical Physics51, 112001 (2018)

    work page 2018

  49. [49]

    Z.-H. Liu, Y. Liu, G.-H. Liang, C.-L. Deng, K. Chen, Y.-H. Shi, T.-M. Li, L. Zhang, B.-J. Chen, C.-P. Fang, et al., Prethermalization by random multipolar driving on a 78-qubit superconducting processor, arXiv preprint arXiv:2503.21553 (2025)

    work page arXiv 2025

  50. [50]

    T. J. Park and J. Light, Unitary quantum time evolution by iterative lanczos reduction, The Journal of chemical physics85, 5870 (1986)

    work page 1986

  51. [51]

    Saad,Iterative methods for sparse linear systems (SIAM, 2003)

    Y. Saad,Iterative methods for sparse linear systems (SIAM, 2003)

    work page 2003

  52. [52]

    Haegeman, J

    J. Haegeman, J. I. Cirac, T. J. Osborne, I. Piˇ zorn, H. Ver- schelde, and F. Verstraete, Time-dependent variational principle for quantum lattices, Physical review letters 107, 070601 (2011)

    work page 2011

  53. [53]

    Koffel, M

    T. Koffel, M. Lewenstein, and L. Tagliacozzo, Entangle- ment entropy for the long-range ising chain in a trans- verse field, Physical review letters109, 267203 (2012)

    work page 2012

  54. [54]

    Goto and I

    S. Goto and I. Danshita, Performance of the time- dependent variational principle for matrix product states in the long-time evolution of a pure state, Physical Re- view B99, 054307 (2019)

    work page 2019

  55. [55]

    Tutunnikov, C

    I. Tutunnikov, C. Chuang, and J. Cao, Coherent spatial control of wave packet dynamics on quantum lattices, The Journal of Physical Chemistry Letters14, 11632 (2023)

    work page 2023

  56. [56]

    Zhang, X.-D

    K.-L. Zhang, X.-D. Jiang, and Y.-Y. Li, Two-doublon bloch oscillations in the mass-imbalanced extended fermi- hubbard model, Physical Review B110, 184304 (2024)

    work page 2024

  57. [57]

    Zatelli, C

    F. Zatelli, C. Benedetti, and M. G. Paris, Scattering as a quantum metrology problem: A quantum walk approach, Entropy22, 1321 (2020)

    work page 2020

  58. [58]

    Typical parameters yield a ra- tio ofu= 40 (e.g.,J/(2π) = 5MHz andU/(2π) = −200MHz)

    Standard transmon qubits naturally possess a negative anharmonicity, realizing the Bose-Hubbard model with attractive interactions. Typical parameters yield a ra- tio ofu= 40 (e.g.,J/(2π) = 5MHz andU/(2π) = −200MHz). However, simulatingu= 40 requires tracking the evolution over prohibitively long timescales due to the extremely small effective pair-hoppin...

    work page

  59. [59]

    Peres, Separability criterion for density matrices, Phys

    A. Peres, Separability criterion for density matrices, Phys. Rev. Lett.77, 1413 (1996)

    work page 1996

  60. [60]

    Vidal and R

    G. Vidal and R. F. Werner, Computable measure of en- tanglement, Phys. Rev. A65, 032314 (2002). 14

    work page 2002

  61. [61]

    Trotzky, Y.-A

    S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollw¨ ock, J. Eisert, and I. Bloch, Probing the re- laxation towards equilibrium in an isolated strongly cor- related one-dimensional bose gas, Nature physics8, 325 (2012)

    work page 2012

  62. [62]

    Schreiber, S

    M. Schreiber, S. S. Hodgman, P. Bordia, H. P. L¨ uschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Observation of many-body localization of inter- acting fermions in a quasirandom optical lattice, Science 349, 842 (2015)

    work page 2015

  63. [63]

    Brydges, A

    T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Probing r´ enyi entanglement entropy via random- ized measurements, Science364, 260 (2019)

    work page 2019

  64. [64]

    A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, Quantum ther- malization through entanglement in an isolated many- body system, Science353, 794 (2016)

    work page 2016

  65. [65]

    Huang, R

    H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measure- ments, Nature Physics16, 1050 (2020)

    work page 2020

  66. [66]

    B. Paul, S. Mondal, and T. Mishra, Anomalous slow- down of the bound state dynamics in a non-locally cou- pled quantum circuit, arXiv preprint arXiv:2506.09818 (2025)

    work page arXiv 2025

  67. [67]

    Bianchetti, S

    R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, C. Lang, L. Steffen, M. Boissonneault, A. Blais, and A. Wallraff, Control and tomography of a three level superconducting artificial atom, Phys. Rev. Lett.105, 223601 (2010)

    work page 2010

  68. [68]

    Roushan, C

    P. Roushan, C. Neill, J. Tangpanitanon, V. M. Bastidas, A. Megrant, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth,et al., Spectroscopic signatures of localiza- tion with interacting photons in superconducting qubits, Science358, 1175 (2017)

    work page 2017

  69. [69]

    Yan, Y.-R

    Z. Yan, Y.-R. Zhang, M. Gong, Y. Wu, Y. Zheng, S. Li, C. Wang, F. Liang, J. Lin, Y. Xu,et al., Strongly cor- related quantum walks with a 12-qubit superconducting processor, Science364, 753 (2019)

    work page 2019

  70. [70]

    Ye, Z.-Y

    Y. Ye, Z.-Y. Ge, Y. Wu, S. Wang, M. Gong, Y.-R. Zhang, Q. Zhu, R. Yang, S. Li, F. Liang,et al., Propagation and localization of collective excitations on a 24-qubit superconducting processor, Physical review letters123, 050502 (2019)

    work page 2019

  71. [71]

    Wang, S.-Y

    Z. Wang, S.-Y. Zhou, Y.-H. Shi, K. Huang, Z. Yang, J. Zhang, K. Zhao, Y. Xu, H. Li, S. Zhao,et al., Ob- serving two-particle correlation dynamics in tunable su- perconducting bose-hubbard simulators, arXiv preprint arXiv:2509.02180 (2025)

    work page arXiv 2025

  72. [72]

    Ticea, E

    N. Ticea, E. Portoles, E. Rosenberg, A. Schuckert, A. Szasz, B. Kobrin, N. Pomata, P. Praneel, C. Miao, S. Kumar, E. Crane, I. Drozdov, Y. Lensky, S. Gonzalez- Garcia, T. Kiely, D. Abanin, A. Abbas, R. Acharya, L. A. Beni, G. Aigeldinger, R. Alcaraz, S. Alcaraz, M. Ans- mann, F. Arute, K. Arya, W. Askew, N. Astrakhant- sev, J. Atalaya, R. Babbush, B. Ball...

    work page arXiv 2025

  73. [73]

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the cooper pair box, Physical Review A—Atomic, Molecular, and Optical Physics76, 042319 (2007)

    work page 2007

  74. [74]

    Eckardt, Colloquium: Atomic quantum gases in pe- riodically driven optical lattices, Rev

    A. Eckardt, Colloquium: Atomic quantum gases in pe- riodically driven optical lattices, Rev. Mod. Phys.89, 011004 (2017). 15

    work page 2017

  75. [75]

    L. B. Nguyen, Y. Kim, A. Hashim, N. Goss, B. Marinelli, B. Bhandari, D. Das, R. K. Naik, J. M. Kreikebaum, A. N. Jordan,et al., Programmable heisenberg inter- actions between floquet qubits, Nature Physics20, 240 (2024)

    work page 2024

  76. [76]

    Lambert, E

    N. Lambert, E. Gigu‘ere, P. Menczel, B. Li, P. Hopf, G. Su’arez, M. Gali, J. Lishman, R. Gadhvi, R. Agarwal, A. Galicia, N. Shammah, P. Nation, J. R. Johansson, S. Ahmed, S. Cross, A. Pitchford, and F. Nori, Qutip 5: The quantum toolbox in Python, Physics Reports1153, 1 (2026)

    work page 2026

  77. [77]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor Software Library for Tensor Network Calcula- tions, SciPost Phys. Codebases , 4 (2022)

    work page 2022

  78. [78]

    Bezanson, A

    J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, Julia: A fresh approach to numerical computing, SIAM Review59, 65 (2017)

    work page 2017