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Exact spectral properties of Fermi polarons in one-dimensional lattices: Anomalous Fermi singularities and polaron quasiparticles

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Pith's one-line read A single mobile impurity in a one-dimensional lattice Fermi gas, at large momentum, develops anomalous Fermi singularities with low-energy power-law tails and broad polaron quasiparticle peaks that are collectively generated by many…

desk verdict Solid exact Bethe-ansatz spectral function for the 1D Hubbard polaron with a convincing Q=0 benchmark, but the central 'coexistence' claim rests on a finite-size exponent that doesn't yet extrapolate to zero. read the letter →

arxiv 2411.17895 v2 pith:56HIMNXS submitted 2024-11-26 cond-mat.quant-gas cond-mat.str-el

Hui Hu , Jia Wang , Xia-Ji Liu This is my paper · ORCID
classification cond-mat.quant-gascond-mat.str-el PACS 71.38.-k71.10.Fd03.75.Ss05.30.Fk
keywords Fermipolaronone-dimensionalHubbardmodelBetheansatzspectralfunctionedgesingularityquasiparticleformfactoropticallattice
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 establishes that the spectral function of a single mobile impurity in a one-dimensional lattice Fermi gas contains two previously unrecognized features at large impurity momentum: anomalous Fermi singularities, whose power-law tails extend to low energy at the Brillouin-zone boundary, and broad polaron quasiparticle peaks that are generated collectively by many excited many-body states rather than by a single dominant state. The results are derived exactly from the Bethe-ansatz solution of the one-dimensional Hubbard model, with explicit form factors computed for regular Bethe states and for the irregular spin-flip and eta-pairing states. Near quarter filling and momentum Q=π, the anomalous singularities and the polaron peaks coexist in the spectrum, a situation with no analogue in two or three dimensions. If the results are right, they provide benchmark spectra for approximate polaron theories and a concrete prediction for cold-atom Ramsey interferometry in optical lattices.

What carries the argument

The central object is the Bethe-ansatz form factor: the overlap of an eigenstate of the one-dimensional Hubbard model with the non-interacting state in which the impurity is a plane wave and the bath fermions form a Fermi sea. The authors write this overlap as an (N+1)×(N+1) determinant, using a Slater-determinant identity, and obtain the norm of the Bethe wavefunction from the same determinant structure. The machinery also includes a full classification of the eigenstates — real-k, k−Λ, spin-flip, and η-pairing — so that the sum over states in the spectral function is nearly complete, and a sum rule ρ_s > 99.8% certifies the truncation at three pseudo particle-hole pairs.

What would settle it

An independent, untruncated calculation of A(Q=π,ω) at quarter filling with U=4t — for instance, by time-dependent density-matrix renormalization group or by including four or more particle-hole pairs in the Bethe sum — should reproduce the anomalous low-energy tail and a polaron peak whose height stays finite as the broadening δ→0. Alternatively, a cold-atom Ramsey interferometry measurement of an impurity accelerated to momentum Q=π in a one-dimensional optical lattice at quarter filling should show the predicted power-law tail and the collective peak; if the tail vanishes or the peak height scales like a singularity exponent, the central claim fails.

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Extended reading notes

Core claim

Using the Lieb-Wu Bethe ansatz for the Hubbard model with one spin-down impurity and N spin-up fermions, the authors derive determinant expressions for the form factor of every eigenstate: the overlap of a Bethe state with the non-interacting product of a plane-wave impurity and a Fermi sea. This includes regular states with real quasi-momenta, k−Λ states with a complex momentum pair, and the irregular spin-flip and η-pairing states. The impurity spectral function A(Q,ω) is then obtained as a sum over roughly half a million states (up to three pseudo particle-hole pairs, with sum rule above 99.8 percent) with a Lorentzian broadening δ=4t/L. At zero momentum the spectrum shows the two conventional power-law Fermi edge singularities; as Q increases each singularity becomes two-sided, and at Q=π the high-energy side disappears, leaving anomalous singularities with low-energy power-law tails. Near quarter filling a broad polaron peak appears at ω≈3t for U=4t, built from many states with residue around $10^{-3}$ (a second bundle near ω≈6t is masked by the upper singularity); finite-size scaling of the peak height distinguishes this collective polaron peak (exponent α≈0.31, decreasing toward 0) from the singularities (α≈0.50 and α≈0.89).

Load-bearing premise

The calculation's load-bearing premise is that the spectral function is converged after summing only up to three pseudo particle-hole pairs (about half a million states) at finite sizes L=20–100, so that the thermodynamic-limit singularities and the polaron peak identified by finite-size scaling with a chosen broadening δ=4t/L are not artifacts of the truncation.

Editorial extensions

If this is right

  • At Q=π and quarter filling, the impurity spectrum simultaneously shows an anomalous Fermi singularity and a polaron quasiparticle peak; both are exact predictions of the Bethe ansatz.
  • The polaron peak is collective: no single eigenstate carries it, so conventional single-pole quasiparticle language (one dominant residue) does not describe it.
  • Finite-size scaling distinguishes the two kinds of features: peak heights of singularities diverge as δ^{-α} with α≈0.89 and 0.50, while the polaron peak's exponent is much smaller (≈0.31, decreasing to ≈0.17 with smaller broadening), consistent with a constant height in the thermodynamic limit.
  • The Chevy variational ansatz with two-particle-hole excitations reproduces the polaron peak, giving a benchmark for approximate many-body theories.
  • The same spectral structure appears for attractive interactions U=-4t under a particle-hole transformation, indicating the coexistence is a generic feature of the one-dimensional lattice polaron, independent of the sign of interaction.

Reading between the lines

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

  • If the collective polaron peak is genuine, the conventional notion of quasiparticle weight (the largest single residue) may need to be replaced by an integrated 'bundle weight' over a small energy window; its scaling with system size could define a new diagnostic for quasiparticles in integrable systems.
  • The same determinant form-factor technique, applied to two impurities, could reveal whether the anomalous singularities persist and how the collective polaron peaks hybridize; the paper's hint at spin-charge separation suggests spinon contributions would appear in the two-impurity spectrum near Q=0 or Q=π.
  • A concrete experimental test: measure the Ramsey overlap S(t) after rapidly transferring an impurity to momentum Q=π; the power-law exponent of the decay tail should match the anomalous singularity exponent α≈0.89, while the polaron peak should appear as a slowly decaying component at a different frequency.
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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

2 major / 4 minor

Summary. Using the Bethe-ansatz solution of the one-dimensional Hubbard model, the authors derive explicit form factors for the overlap between the non-interacting impurity-plus-Fermi-sea product state and the regular Bethe states, as well as the irregular spin-flip and eta-pairing states. They then evaluate the impurity spectral function A(Q,omega) on finite lattices by summing over states with up to three pseudo particle-hole pairs, and analyze the resulting spectra for various momenta and fillings. The main findings are: (i) at small momentum the spectrum shows two power-law Fermi-edge singularities, with the Q=0 exponent matching the known Castella-Zotos value; (ii) at large momentum the singularities become two-sided and eventually, at Q=pi, develop into 'anomalous' Fermi singularities with low-energy-oriented power-law tails; and (iii) near quarter filling, two broad peaks at large momentum are interpreted as polaron quasiparticles collectively generated by many states. The classification of the singularities and the purported polaron peaks rests on finite-size scaling of peak heights A_max ~ delta^{-alpha}, with exponents alpha=0.89 and 0.50 for the singularities and alpha=0.31 (for delta=4t/L) or 0.17 (for delta=t/L) for the claimed polaron peak.

Significance. If established, this work provides the first exact Bethe-ansatz spectral function for lattice Fermi polarons including the contributions of irregular spin-flip and eta-pairing states, and it uncovers a qualitatively new spectral structure at large momentum that is absent in higher dimensions. The paper has clear strengths: the form-factor derivation is nontrivial, the sum rule exceeds 99.8%, the Q=0 singularity exponent (alpha_fit=0.871) agrees with the independent analytical value (0.875), and the Chevy-ansatz comparison gives a useful benchmark. However, the central novelty—the coexistence of anomalous Fermi singularities with polaron quasiparticles—is only as convincing as the evidence that the second peak is not itself a power-law singularity. The finite-size scaling data show a nonzero exponent for both broadening choices, and the extrapolation to zero is not controlled. Thus the significance would be greatly enhanced by a more rigorous identification of the polaron peak, either through a controlled scaling that isolates the overlap with the adjacent singularity or through a quantity that directly distinguishes a true quasiparticle from a power-law singularity.

major comments (2)
  1. [Appendix B, Figs. 6-7] The classification of peak II as a polaron quasiparticle, rather than as a power-law singularity, is load-bearing for the central claim of coexistence. The finite-size scaling in Figs. 6(b) and 7 yields alpha_II = 0.31 for delta = 4t/L and alpha_II = 0.17 for delta = t/L, both clearly nonzero. The sentence 'It is reasonable to believe that, by taking the limit delta -> 0 with more numerical efforts, we might eventually confirm alpha_II = 0' is an unsupported extrapolation from three data points without error bars and without a model for the overlap with singularity I that the authors themselves invoke to explain the L-dependence. A nonzero alpha_II would imply that peak II is itself a power-law singularity with vanishing integrated weight in the thermodynamic limit, which would invalidate the coexistence claim. The authors should either provide a controlled scaling that explicitly removes the overlap contribution and shows alpha_II -> 0, or measure a quantity that distinguishes a quasiparticle from a singularity, such as the integrated spectral weight under peak II as a function of L (a delta-function peak has finite weight, whereas a power law with 0<alpha<1 has weight scaling as delta^{1-alpha} -> 0).
  2. [Spectral function section (page 3)] The paper repeatedly calls the result 'exact', but the sum in Eq. (4) is truncated to three pseudo particle-hole pairs. The stated sum rule rho_s > 99.8% bounds the total omitted residue, but it does not by itself guarantee that the omitted states contribute negligibly to a specific feature such as peak II, whose total weight may be only a few percent of the total spectral weight. A convergence check (e.g., comparing the spectral function and the peak height with truncations at two and three pairs, or reporting the integrated weight under peak II as a function of L) is needed to support the statement that 'the omitted states have negligible effect on the convergence of our numerics' and to secure the polaron classification.
minor comments (4)
  1. [Page 3, near Fig. 3] The phrase 'the leftest hole state' should be corrected to 'the leftmost hole state'.
  2. [Caption of Fig. 2] The phrase 'eight-spoked asterisks' is awkward; consider 'eight-pointed asterisks' or simply 'asterisks'.
  3. [Eq. (4) and spectral function section] The broadening factor delta = 4t/L is introduced without justification; a brief comment on the sensitivity of the results to this choice (partly addressed in Appendix B) would be helpful for reproducibility.
  4. [Abstract and Introduction] The term 'exact spectral function' is used despite the truncation to three pseudo particle-hole pairs; consider using 'numerically exact' or 'highly accurate' to align the wording with the stated limitation in the spectral function section.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Bethe-ansatz spectral function is derived from the exact Lieb-Wu eigenstates with no parameters fitted to the claimed spectral features, and the central singularities are anchored to an independent external result.

full rationale

The paper's central derivation is self-contained: Eq. (4) defines the spectral function directly from the exactly computed form factors of the Lieb-Wu Bethe states, with the only input parameters being the model parameters L, N, U, t, and Q. No parameter is fitted to the target spectral features, and none of the claimed predictions (anomalous Fermi singularities I and III, polaron peaks II and IV) is used to define the inputs. The Q=0 Fermi-edge exponent is checked against the independent analytical formula of Ref. [38] (external to the authors), giving a numerical slope 0.871 versus the analytical value 0.875, so the method has an external anchor. The self-citations (Ref. [26] for the Chevy comparison and Ref. [49] for solving the Bethe equations) are technical or comparative tools, not load-bearing premises for the coexistence claim. The finite-size scaling of the polaron peak, where alpha_II = 0.31 or 0.17 and the authors state it is 'reasonable to believe' alpha_II = 0, is an extrapolation and a robustness concern, not a circular reduction: the exponent is diagnosed after the spectral function is computed, and the polaron classification is an interpretation of the data rather than an input to it. Thus no step in the derivation chain reduces by construction to its own inputs.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central calculation depends on standard Bethe ansatz completeness plus several numerical choices: the broadening delta, the truncation order, and the finite-size scaling exponents used to classify the spectral features. These are not parameters fitted to experimental data, but they are chosen or fitted by the authors and the classification of the polaron peak depends on an extrapolation. No new physical entities are introduced.

free parameters (3)
  • Broadening factor delta = 4t/L, and t/L in Appendix B
    Chosen by hand to smooth the discrete finite-size spectrum. It directly sets the peak heights Amax and the exponents alpha extracted in the finite-size scaling analysis.
  • Truncation order of Bethe-state sum = three pseudo particle-hole pairs
    Numerical cutoff for the spectral function sum. The authors assert a sum rule above 99.8 percent but do not show a convergence scan specifically for the Q = pi polaron peak.
  • Fitted scaling exponents alpha for feature classification = alpha_I ~ 0.50, alpha_II ~ 0.31 (or 0.17 with delta = t/L), alpha_III ~ 0.89
    These exponents are fitted to ln Amax versus ln delta data and used to label features as Fermi singularities or polarons. The nonzero alpha_II means the polaron interpretation depends on an extrapolation to delta = 0.
assumptions (4)
  • domain assumption The 1D Hubbard model Bethe ansatz eigenstates, including irregular spin-flip and eta-pairing states, form a complete basis for the single-impurity sector.
    Invoked when summing over regular and irregular states in Eq. (4); completeness relies on integrability results from Essler, Korepin, and Schoutens [41].
  • standard math The overlap of two Slater determinants is correctly computed by the determinant identity in Eq. (3).
    Standard quantum chemistry identity used to derive the form factor; reference [52] is cited.
  • ad hoc to paper Truncating the sum at three pseudo particle-hole pairs with sum rule rho_s > 99.8 percent leaves negligible contributions to all reported spectral features.
    The authors state that omitted states have negligible effect, but no explicit convergence study is shown for the Q = pi polaron peaks.
  • domain assumption Finite-size scaling of peak heights Amax proportional to delta^{-alpha} correctly identifies thermodynamic-limit singularities and distinguishes them from polarons with alpha = 0.
    Used in Appendix B to classify features. The extracted alpha_II = 0.17 for the polaron peak is nonzero, so the interpretation relies on extrapolation to delta = 0.

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Pith. "Pith review of Exact spectral properties of Fermi polarons in one-dimensional lattices: Anomalous Fermi singularities and polaron quasiparticles." pith.science (2026). https://pith.science/paper/56HIMNXS

@misc{pith2026241117895,
  author       = {Pith},
  title        = {Pith review of: Exact spectral properties of Fermi polarons in one-dimensional lattices: Anomalous Fermi singularities and polaron quasiparticles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/56HIMNXS}},
  note         = {Machine review of arXiv:2411.17895}
}
abstract

We calculate the exact spectral function of a single impurity repulsively interacting with a bath of fermions in one-dimensional lattices, by deriving the explicit expression of the form factor for both regular Bethe states and the irregular spin-flip state and $\eta$-pairing state, based on the exactly solvable Lieb-Wu model. While at low impurity momentum $Q\sim0$ the spectral function is dominated by two power-law Fermi singularities, at large momentum we observe that the two singularities develop into two-sided distributions and eventually become anomalous Fermi singularities at the boundary of the Brillouin zone (i.e., $Q=\pm\pi$), with the power-law tails extending towards low energy. Near the quarter filling of the Fermi bath, we also find two broad polaron peaks at large impurity momentum, collectively contributed by many excited many-body states with non-negligible form factors. Our exact results of those distinct features in one-dimensional Fermi polarons, which have no correspondences in two and three dimensions, could be readily probed in cold-atom laboratories by trapping highly imbalanced two-component fermionic atoms into one-dimensional optical lattices.

Figures

Figures reproduced from arXiv: 2411.17895 by the authors.

Figure 1
Figure 1. FIG. 1. The contour plot of the impurity spectral function [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Residues (a1, b1 and c1) and the impurity spectral functions (a2, b2 and c2, in units of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Residues (b) and the impurity spectral function (c, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Impurity spectral function [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. ln [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 6
Figure 6. Figure 6: FIG. 6. ln [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

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Works this paper leans on

56 extracted references · 45 canonical work pages

  1. [1]

    A. S. Alexandrov and J. T. Devreese, Advances in Po- laron Physics (Springer, New York, 2010), Vol. 159

    work page 2010

  2. [2]

    P. W. Anderson, Infrared Catastrophe in Fermi Gases with Local Scattering Potentials, Phys. Rev. Lett. 18, 1049 (1967)

    work page 1967

  3. [3]

    G. D. Mahan, Excitons in Metals: Infinite Hole Mass, Phys. Rev. 163, 612 (1967)

    work page 1967

  4. [4]

    Nozi` eres and C

    P. Nozi` eres and C. T. De Dominicis, Singularities in the X-Ray Absorption and Emission of Metals. III. One- Body Theory Exact Solution, Phys. Rev. 178, 1097 (1969)

    work page 1969

  5. [5]

    Nagaoka, Ferromagnetism in a Narrow, Almost Half- Filled s Band, Phys

    Y. Nagaoka, Ferromagnetism in a Narrow, Almost Half- Filled s Band, Phys. Rev. 147, 392 (1966)

    work page 1966

  6. [6]

    Massignan, M

    P. Massignan, M. Zaccanti, and G. M. Bruun, Polarons, dressed molecules and itinerant ferromagnetism in ultra- cold Fermi gases, Rep. Prog. Phys. 77, 034401 (2014)

    work page 2014

  7. [7]

    Schmidt, M

    R. Schmidt, M. Knap, D. A. Ivanov, J.-S. You, M. Cetina, and E. Demler, Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress, Rep. Prog. Phys. 81, 024401 (2018)

    work page 2018

  8. [8]

    Wang, Functional determinant approach investigations of heavy impurity physics, AAPPS Bull

    J. Wang, Functional determinant approach investigations of heavy impurity physics, AAPPS Bull. 33, 20 (2023)

    work page 2023

Show all 56 references
  1. [9]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008)

    2008

  2. [10]

    C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Fesh- bach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010)

    2010

  3. [11]

    Schirotzek, C.-H

    A. Schirotzek, C.-H. Wu, A. Sommer, and M.W. Zwier- lein, Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms, Phys. Rev. Lett. 102, 230402 (2009)

    2009

  4. [12]

    Zhang, W

    Y. Zhang, W. Ong, I. Arakelyan, and J. E. Thomas, Polaron-to-Polaron Transitions in the Radio-Frequency Spectrum of a Quasi-Two-Dimensional Fermi Gas, Phys. Rev. Lett. 108, 235302 (2012)

    2012

  5. [13]

    Z. Yan, P. B. Patel, B. Mukherjee, R. J. Fletcher, J. Struck, and M.W. Zwierlein, Boiling a Unitary Fermi Liquid, Phys. Rev. Lett. 122, 093401 (2019)

    2019

  6. [14]

    Cetina, M

    M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M.Walraven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, and E. Demler, Ultrafast many-body interferometry of impurities coupled to a Fermi sea, Sci- ence 354, 96 (2016)

    2016

  7. [15]

    Scazza, G

    F. Scazza, G. Valtolina, P. Massignan, A. Recati, A. Am- ico, A. Burchianti, C. Fort, M. Inguscio, M. Zaccanti, and G. Roati, Repulsive Fermi Polarons in a Resonant Mixture of Ultracold 6Li Atoms, Phys. Rev. Lett. 118, 083602 (2017)

    2017

  8. [16]

    F. J. Vivanco, A. Schuckert, S. Huang, G. L. Schu- macher, G. G. T. Assump¸ c˜ ao, Y. Ji, J. Chen, M. Knap, and Nir Navon, The strongly driven Fermi polaron, arXiv:2308.05746

    arXiv

  9. [17]

    G. Ness, C. Shkedrov, Y. Florshaim, O. K. Diessel, J. von Milczewski, R. Schmidt, and Y. Sagi, Observation of a Smooth Polaron-Molecule Transition in a Degenerate Fermi Gas, Phys. Rev. X 10, 041019 (2020)

    2020

  10. [18]

    Chevy, Universal phase diagram of a strongly interact- ing Fermi gas with unbalanced spin populations, Phys

    F. Chevy, Universal phase diagram of a strongly interact- ing Fermi gas with unbalanced spin populations, Phys. Rev. A 74, 063628 (2006)

    2006

  11. [19]

    Combescot and S

    R. Combescot and S. Giraud, Normal State of Highly Po- larized Fermi Gases: Full Many-Body Treatment, Phys. Rev. Lett. 101, 050404 (2008)

    2008

  12. [20]

    M. M. Parish and J. Levinsen, Highly polarized Fermi gases in two dimensions, Phys. Rev. A87, 033616 (2013)

    2013

  13. [21]

    W. E. Liu, J. Levinsen, and M. M. Parish, Variational Approach for Impurity Dynamics at Finite Temperature, Phys. Rev. Lett. 122, 205301 (2019)

    2019

  14. [22]

    Combescot, A

    R. Combescot, A. Recati, C. Lobo, and F. Chevy, Normal State of Highly Polarized Fermi Gases: Simple Many- Body Approaches, Phys. Rev. Lett. 98, 180402 (2007)

    2007

  15. [23]

    H. Hu, B. C. Mulkerin, J. Wang, and X.-J. Liu, Attrac- tive Fermi polarons at nonzero temperatures with a finite impurity concentration, Phys. Rev. A 98, 013626 (2018)

    2018

  16. [24]

    Tajima and S

    H. Tajima and S. Uchino, Thermal crossover, transition, and coexistence in Fermi polaronic spectroscopies, Phys. Rev. A 99, 063606 (2019)

    2019

  17. [25]

    Hu and X.-J

    H. Hu and X.-J. Liu, Fermi polarons at finite tempera- ture: Spectral function and rf spectroscopy, Phys. Rev. A 105, 043303 (2022)

    2022

  18. [26]

    H. Hu, J. Wang, and X.-J. Liu, Theory of the spectral function of Fermi polarons at finite temperature, Phys. Rev. Lett. 133, 083403 (2024)

    2024

  19. [27]

    Schmidt and T

    R. Schmidt and T. Enss, Excitation spectra and rf response near the polaron-to-molecule transition from the functional renormalization group, Phys. Rev. A 83, 063620 (2011)

    2011

  20. [28]

    von Milczewski and R

    J. von Milczewski and R. Schmidt, Momentum- dependent quasiparticle properties of the Fermi polaron from the functional renormalization group, Phys. Rev. A 110, 033309 (2024)

    2024

  21. [29]

    Prokof’ev and B

    N. Prokof’ev and B. Svistunov, Fermi-polaron problem: Diagrammatic Monte Carlo method for divergent sign- alternating series, Phys. Rev. B 77, 020408(R) (2008)

    2008

  22. [30]

    Goulko, A

    O. Goulko, A. S. Mishchenko, N. Prokof’ev, and B. Svis- tunov, Dark continuum in the spectral function of the resonant Fermi polaron, Phys. Rev. A 94, 051605(R) (2016)

    2016

  23. [31]

    Ramachandran, S

    S. Ramachandran, S. Jensen, Y. Alhassid, Precision Thermodynamics of the Fermi polaron at strong cou- pling, arXiv:2410.00886

  24. [32]

    M. Knap, A. Shashi, Y. Nishida, A. Imambekov, D. A. Abanin, and E. Demler, Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Be- yond, Phys. Rev. X 2, 041020 (2012). 8

    2012

  25. [33]

    Wang, X.-J

    J. Wang, X.-J. Liu, and H. Hu, Exact Quasiparticle Properties of a Heavy Polaron in BCS Fermi Superflu- ids, Phys. Rev. Lett. 128, 175301 (2022)

    2022

  26. [34]

    Wang, X.-J

    J. Wang, X.-J. Liu, and H. Hu, Heavy polarons in ultra- cold atomic Fermi superfluids at the BEC-BCS crossover: Formalism and applications, Phys. Rev. A 105, 043320 (2022)

    2022

  27. [35]

    E. H. Lieb and F. Y. Wu, Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension, Phys. Rev. Lett. 20, 1445 (1968)

    1968

  28. [36]

    Deguchi, F

    T. Deguchi, F. H. L. Essler, F. G¨ ohmann, A. Kl¨ umper,V. E. Korepin and K. Kusakabe, Thermodynamics and ex- citations of the one-dimensional Hubbard model, Phys. Rep. 331, 197 (2000)

    2000

  29. [37]

    F. H. L. Essler, H. Frahm, F. G¨ ohmann, A. Kl¨ umper, and V. E. Korepin, The One-Dimensional Hubbard Model (Cambridge University Press, New York, 2005)

    2005

  30. [38]

    by calculating the ground-state form factor of the exactly solvable continuous Gaudin-Yang model [39]. Here, we generalize the pioneering work [38] to the 1D Hubbard model and calculate the form factors of all the excited many-body states, including the spin-flip state and η-p...

    2025 arXiv

  31. [39]

    J. B. McGuire, Interacting fermions in one dimension. II. Attractive potential, J. Math. Phys. 7, 123 (1966)

    1966

  32. [40]

    Castella and X

    H. Castella and X. Zotos, Exact calculation of spec- tral properties of a particle interacting with a one- dimensional fermionic system, Phys. Rev. B 47, 16186 (1993)

    1993

  33. [41]

    F. H. L. Essler, V. E. Korepin, and K. Schoutens, New eigenstates of the 1-dimensional Hubbard model, Nucl. Phys. B 372, 559 (1992)

    1992

  34. [42]

    Here, we adopt a single- particle wavefunction χj(y) that is more suitable to han- dle the k − Λ solutions with a pair of complex-valued quasi-momenta [51]

    in the Gaudin-Yang model. Here, we adopt a single- particle wavefunction χj(y) that is more suitable to han- dle the k − Λ solutions with a pair of complex-valued quasi-momenta [51]. Form factor. We are interested in the form fac- tor or the overlap FN +1({kj}, Λ) of the Bethe...

  35. [43]

    C. N. Yang, η pairing and off-diagonal long-range order in a Hubbard model, Phys. Rev. Lett. 63, 2144 (1989)

    1989

  36. [44]

    C. J. M. Mathy, M. B. Zvonarev, and E. Demler, Quan- tum flutter of supersonic particles in one-dimensional quantum liquids, Nat. Phys. 8, 881 (2012)

    2012

  37. [45]

    M. Knap, C. J. M. Mathy, M. Ganahl, M. B. Zvonarev, and E. Demler, Quantum Flutter: Signatures and Ro- bustness, Phys. Rev. Lett. 112, 015302 (2014)

    2014

  38. [46]

    Gamayun, O

    O. Gamayun, O. Lychkovskiy, E. Burovski, M. Malcom- son, V. V. Cheianov, and M. B. Zvonarev, Impact of the Injection Protocol on an Impurity’s Stationary State, Phys. Rev. Lett. 120, 220605 (2018)

    2018

  39. [47]

    P. E. Dolgirev, Y.-F. Qu, M. B. Zvonarev, T. Shi, and E. Demler, Emergence of a Sharp Quantum Collective Mode in a One-Dimensional Fermi Polaron, Phys. Rev. X 11, 041015 (2021)

    2021

  40. [48]

    Zhang, Y

    Z.-H. Zhang, Y. Jiang, H.-Q. Lin, and Xi-Wen Guan, Mi- croscopic origin of the quantum supersonic phenomenon in one dimension, Phys. Rev. A 110, 023329 (2024)

    2024

  41. [49]

    Kohno, Spectral Properties near the Mott Transi- tion in the One-Dimensional Hubbard Model, Phys

    M. Kohno, Spectral Properties near the Mott Transi- tion in the One-Dimensional Hubbard Model, Phys. Rev. Lett. 105, 106402 (2010)

    2010

  42. [50]

    Our integer quantum number sj is related to Ij by sj = Ij + 1/2

    In the literature, the quasi-momentum kj is specified by a half integer Ij for odd number of N [36, 37, 47]. Our integer quantum number sj is related to Ij by sj = Ij + 1/2

  43. [51]

    Liu and H

    X.-J. Liu and H. Hu, Exact calculation of spectral proper- ties of a particle interacting with a one-dimensional Fermi gas in optical lattices, AAPPS Bull. 35, 9 (2025)

    2025

  44. [52]

    D. M. Edwards, Magnetism in Single-Band Models: Ex- act One-Dimensional Wave Functions Generalised to Higher Dimensions, Prog. Theor. Phys. Suppl. 101, 453 (1990)

    1990

  45. [53]

    Gamayun, A

    O. Gamayun, A. G. Pronko, and M. B. Zvonarev, Im- purity Green’s function of a one-dimensional Fermi gas, Nucl. Phys. B 892, 83 (2015)

    2015

  46. [54]

    Plasser, M

    F. Plasser, M. Ruckenbauer, S. Mai, M. Oppel, P. Mar- quetand, and L. Gonz´ alez, Efficient and Flexible Com- putation of Many-Electron Wave Function Overlaps, J. Chem. Theory Comput. 12, 1207 (2016)

    2016

  47. [55]

    These fast oscillations are not important and should disappear for sufficiently large L

    There are small fast oscillations in the spectral function, due to the discrete eigenstates at finite number of lattice sites L, which can not completely smoothed out by the finite broadening factor δ = 4t/L. These fast oscillations are not important and should disappear for s...

  48. [56]

    Meinert, M

    F. Meinert, M. Knap, E. Kirilov, K. Jag-Lauber, M. B. Zvonarev, E. Demler, and H.-C. N¨ agerl, Bloch Oscilla- tions in the Absence of a Lattice, Science356, 945 (2017)

    2017

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.