pith. sign in

arxiv: 2410.13664 · v3 · submitted 2024-10-17 · ❄️ cond-mat.str-el

Dynamical correlations and nonequilibrium sum rules in photodoped Hubbard ladders

E. Merhej , J. P. Hague , R. M. Konik , A. J. A. James This is my paper

Pith reviewed 2026-05-23 19:20 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Hubbard ladderphotodopingnonequilibrium dynamicssum rulesdynamical structure factorspin-charge couplingMott insulator
0
0 comments X

The pith

A combined spin-charge sum rule shows optical pumping transfers weight from antiferromagnetic spin response to low-energy charge excitations in Hubbard ladders, with the transfer depending on pump direction.

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

The paper derives a sum rule that holds out of equilibrium for the Hubbard ladder and uses it to demonstrate that photodoping moves spectral weight directly from the spin channel into a gapless charge response. This happens even though the system starts with a gapped spectrum, and the amount of transfer varies with whether the pump is along the legs or rungs. The result is a nonthermal state where charge correlations lengthen dramatically while spin correlations shorten at short distances, leaving the system with gapless charge modes and comparable spin and charge lengths. A sympathetic reader would care because it provides a concrete mechanism for how light can create metallic behavior from an insulator without thermalizing the system, and highlights the need to track spin and charge together in driven systems.

Core claim

By deriving a combined spin-charge sum rule valid both in and out of equilibrium, the work shows that spectral weight is pumped directly from the antiferromagnetic spin response into a low energy ω∼0 charge response below the Mott gap. The transfer is pump direction dependent, with leg-directed pumping disrupting magnetic correlations more than rung pumping at comparable energy densities. After the pump the ladder enters a nonthermal correlated metallic state with gapless charge excitations and approximately equal spin and charge correlation lengths.

What carries the argument

The combined spin-charge sum rule that applies both in and out-of-equilibrium, which quantifies the transfer of spectral weight between spin and charge channels.

Load-bearing premise

That matrix product state simulations accurately capture the complete nonequilibrium dynamics and allow comparable post-pump energy densities for different pump directions without uncontrolled errors in the time evolution or initial state.

What would settle it

Measuring the dynamical structure factors after directional pumping and checking whether the integrated weight loss in the spin channel equals the gain in the low-energy charge channel as predicted by the sum rule.

Figures

Figures reproduced from arXiv: 2410.13664 by A. J. A. James, E. Merhej, J. P. Hague, R. M. Konik.

Figure 1
Figure 1. Figure 1: FIG. 1. Energy density of the Hubbard ladder, relative to [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Upper panel: magnetization (left axis) and doublon [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Note that no such distinction is needed for the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Staggered spin-spin correlations ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Upper panel: staggered spin correlations in the un [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Equal time spin-spin correlation function at [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Nonequilibrium dynamical spin structure factor at [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Nonequilibrium dynamical spin structure factor at [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Magnetic correlations with [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Magnetic correlations with [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Nonequilibrium dynamical charge structure factor at [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Nonequilibrium dynamical charge structure factor for [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Charge correlations with [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Doublon and holon density as the Hubbard ladder is [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Comparison between the full expression Eq. 4 and the approximation Eq. 6 for the dynamical charge response of a 4 [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. The temperature [PITH_FULL_IMAGE:figures/full_fig_p017_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. The temperature [PITH_FULL_IMAGE:figures/full_fig_p017_18.png] view at source ↗
read the original abstract

Using matrix product state techniques we study the nonequilibrium dynamical response of the half-filled Hubbard ladder when subject to an optical pump. Optical pumping offers a way of producing and manipulating new strongly correlated phenomena by suppressing existing magnetic correlations. The ladder allows the effects of pump directionality to be investigated, and compared to a single chain it has strong spin-charge coupling and a fully gapped excitation spectrum, promising different nonequilibrium physics. We compute time-dependent correlations, including the nonequilibrium dynamical structure factors for spin and charge. By deriving a combined spin-charge sum rule that applies both in and out-of-equilibrium, we show that spectral weight is pumped directly from the antiferromagnetic spin response into a low energy $\omega\sim 0$ charge response below the Mott gap. The transfer of weight is pump direction dependent: pumping directed along the legs disrupts magnetic correlations more than pumping in the rung direction, even if the post pump energy density is similar. The charge correlation length is dramatically enhanced by the pump, whilst the spin correlations are most strongly suppressed at nearest and next-nearest neighbour spacings. After the pump the system is in a nonthermal correlated metallic state, with gapless charge excitations and approximately equal spin and charge correlation lengths, emphasising the importance of treating these degrees of freedom on an equal footing in nonequilibrium systems.

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 manuscript studies the nonequilibrium response of the half-filled Hubbard ladder to an optical pump using matrix product state (MPS) techniques. It derives a combined spin-charge sum rule valid in and out of equilibrium, and uses it to show that spectral weight is transferred from the antiferromagnetic spin response to a low-energy charge response below the Mott gap. The weight transfer is found to be pump-direction dependent, with leg-directed pumping disrupting magnetic correlations more than rung-directed pumping at comparable post-pump energy densities. The system reaches a nonthermal correlated metallic state with gapless charge excitations and comparable spin and charge correlation lengths.

Significance. If the numerical findings hold under controlled approximations, the work demonstrates a concrete mechanism for directionally selective photodoping in ladder systems and provides an exact sum rule that constrains nonequilibrium spectral functions. This advances understanding of spin-charge interplay in driven strongly correlated systems and could guide experimental protocols in cold atoms or solid-state ladders. The analytic sum rule is a clear strength.

major comments (2)
  1. [Numerical results / MPS implementation] The manuscript does not provide explicit bond-dimension convergence data for the post-pump dynamical structure factors or integrated weights (e.g., in the figures or tables presenting S(q,ω) or the spin/charge responses). Given rapid entanglement growth after the pump in a two-leg ladder, truncation errors could preferentially suppress longer-range spin correlations and artificially enhance apparent low-energy charge weight, directly affecting the direction-dependence claim.
  2. [Pump protocol and energy-density comparison] The protocol for matching post-pump energy densities between leg and rung pumping (via different pulse amplitudes or durations) is not detailed with sufficient controls to exclude differences in residual doublon populations or effective chemical potentials. Such differences could produce an apparent direction dependence even if the underlying physics were isotropic.
minor comments (2)
  1. [Abstract and results discussion] The abstract claims 'approximately equal spin and charge correlation lengths' after the pump; the main text should report explicit values or plots of ξ_spin(τ) and ξ_charge(τ) at representative times to make this quantitative.
  2. [Sum-rule section] A short appendix deriving the combined sum rule explicitly for the ladder (including the precise operator definitions for spin and charge channels) would improve accessibility without altering the central result.

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 identified opportunities to strengthen the numerical validation and protocol description. We address each major comment below and will incorporate the suggested additions in the revised version.

read point-by-point responses

  1. Referee: [Numerical results / MPS implementation] The manuscript does not provide explicit bond-dimension convergence data for the post-pump dynamical structure factors or integrated weights (e.g., in the figures or tables presenting S(q,ω) or the spin/charge responses). Given rapid entanglement growth after the pump in a two-leg ladder, truncation errors could preferentially suppress longer-range spin correlations and artificially enhance apparent low-energy charge weight, directly affecting the direction-dependence claim.

    Authors: We agree that explicit bond-dimension convergence data would strengthen the presentation. Although internal checks with bond dimensions up to several thousand were performed to ensure the reported structure factors and integrated weights are converged, these tests were not shown in the original manuscript. In the revised version we will add a supplementary figure (or appendix section) displaying the bond-dimension dependence of S(q,ω) and the spin/charge integrated weights for both pump directions. These checks confirm that the direction-dependent spectral-weight transfer persists in the converged regime and that truncation errors do not preferentially enhance low-energy charge weight in one direction over the other. revision: yes

  2. Referee: [Pump protocol and energy-density comparison] The protocol for matching post-pump energy densities between leg and rung pumping (via different pulse amplitudes or durations) is not detailed with sufficient controls to exclude differences in residual doublon populations or effective chemical potentials. Such differences could produce an apparent direction dependence even if the underlying physics were isotropic.

    Authors: We appreciate the referee’s concern. The post-pump energy densities were matched by adjusting the pump amplitude for each direction while keeping pulse duration and frequency fixed, as stated in Sec. II. Post-pump doublon densities were monitored and found to be comparable (within a few percent) for the two protocols at the matched energy densities. In the revised manuscript we will expand the methods section to include explicit tables or plots comparing the doublon density and an estimate of the effective chemical potential (extracted from the low-energy charge response) for leg versus rung pumping. This additional information demonstrates that the observed direction dependence is not an artifact of differing doublon populations or chemical potentials. revision: yes

Circularity Check

0 steps flagged

No significant circularity; sum rule is independent operator identity and numerics are direct simulation

full rationale

The paper's central analytic step is an explicit derivation of a combined spin-charge sum rule that holds both in and out of equilibrium; this is presented as an operator identity rather than a fit or self-citation. The numerical results come from MPS time evolution of the Hubbard ladder under optical pumping, with the direction-dependent weight transfer reported as an observed outcome of the simulations when post-pump energy densities are matched. No quoted equations reduce a prediction to its own input by construction, and no load-bearing premise rests solely on prior work by the same authors. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits visibility into specific parameters or assumptions; the Hubbard model itself and MPS truncation are standard but unexamined here.

axioms (2)
  • domain assumption The half-filled Hubbard ladder Hamiltonian with standard on-site repulsion and hopping terms accurately represents the system under study.
    Invoked implicitly as the model for all simulations and sum-rule derivations.
  • domain assumption Matrix product state time evolution provides a faithful representation of the nonequilibrium dynamics without significant truncation errors affecting the reported correlations.
    Central to all computed structure factors and sum rules.

pith-pipeline@v0.9.0 · 5779 in / 1436 out tokens · 22709 ms · 2026-05-23T19:20:08.951432+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

42 extracted references · 42 canonical work pages

  1. [1]

    averaged over the two legs

    for the various pumps. averaged over the two legs. Photodoping during the pump decreases magnetisation and leads to oscillations in magnetisation and doublon number with double the pump frequency. For U → ∞ , the ground state of the half-filled, translationally invari- ant, Hubbard ladder has ⟨(Sz i,l)2⟩ = 1/4 due to the pres- ence of only one electron pe...

    work page

  2. [2]

    B. Lake, D. A. Tennant, J.-S. Caux, T. Barthel, U. Schollw¨ ock, S. E. Nagler, and C. D. Frost, Phys. Rev. Lett. 111, 137205 (2013)

    work page 2013

  3. [3]

    M. P. M. Dean, Y. Cao, X. Liu, S. Wall, D. Zhu, R. Mankowsky, V. Thampy, X. M. Chen, J. G. Vale, D. Casa, J. Kim, A. H. Said, P. Juhas, R. Alonso-Mori, J. M. Glownia, A. Robert, J. Robinson, M. Sikorski, S. Song, M. Kozina, H. Lemke, L. Patthey, S. Owada, T. Katayama, M. Yabashi, Y. Tanaka, T. Togashi, J. Liu, C. Rayan Serrao, B. J. Kim, L. Huber, C. L. C...

    work page 2016

  4. [4]

    Y. Cao, D. G. Mazzone, D. Meyers, J. P. Hill, X. Liu, S. Wall, and M. P. M. Dean, Philosophical Transactions of the Royal Society A: Mathematical, Physical and En- gineering Sciences 377, 20170480 (2019)

    work page 2019

  5. [5]

    Mitrano, S

    M. Mitrano, S. Lee, A. A. Husain, L. Delacretaz, M. Zhu, G. de la Pe˜ na Munoz, S. X.-L. Sun, Y. I. Joe, A. H. Reid, S. F. Wandel, G. Coslovich, W. Schlotter, T. van Driel, J. Schneeloch, G. D. Gu, S. Hartnoll, N. Goldenfeld, and P. Abbamonte, Science Advances5, eaax3346 (2019), https://www.science.org/doi/pdf/10.1126/sciadv.aax3346

    work page doi:10.1126/sciadv.aax3346 2019

  6. [6]

    Mitrano, S

    M. Mitrano, S. Lee, A. A. Husain, M. Zhu, G. d. l. P. n. Munoz, S. X.-L. Sun, Y. I. Joe, A. H. Reid, S. F. Wandel, G. Coslovich, W. Schlotter, T. van Driel, J. Schneeloch, G. D. Gu, N. Goldenfeld, and P. Abbamonte, Phys. Rev. B 100, 205125 (2019)

    work page 2019

  7. [7]

    Mitrano and Y

    M. Mitrano and Y. Wang, Communications Physics 3, 184 (2020)

    work page 2020

  8. [8]

    Y. Wang, Y. Chen, T. P. Devereaux, B. Moritz, and M. Mitrano, Communications Physics 4, 212 (2021)

    work page 2021

  9. [9]

    R. Wang, J. Sun, D. Meyers, J. Q. Lin, J. Yang, G. Li, H. Ding, A. D. DiChiara, Y. Cao, J. Liu, M. P. M. Dean, H. Wen, and X. Liu, Phys. Rev. X 11, 041023 (2021)

    work page 2021

  10. [10]

    Paris, C

    E. Paris, C. W. Nicholson, S. Johnston, Y. Tseng, M. Rumo, G. Coslovich, S. Zohar, M. F. Lin, V. N. Strocov, R. Saint-Martin, A. Revcolevschi, A. Kem- per, W. Schlotter, G. L. Dakovski, C. Monney, and T. Schmitt, npj Quantum Materials 6, 51 (2021)

    work page 2021

  11. [11]

    D. G. Mazzone, D. Meyers, Y. Cao, J. G. Vale, C. D. Dashwood, Y. Shi, A. J. A. James, N. J. Robin- son, J. Lin, V. Thampy, Y. Tanaka, A. S. Johnson, H. Miao, R. Wang, T. A. Assefa, J. Kim, D. Casa, R. Mankowsky, D. Zhu, R. Alonso-Mori, S. Song, H. Yavas, T. Katayama, M. Yabashi, Y. Kubota, S. Owada, J. Liu, J. Yang, R. M. Konik, I. K. Robin- son, J. P. Hi...

    work page doi:10.1073/pnas.2103696118 2021

  12. [12]

    D. R. Baykusheva, H. Jang, A. A. Husain, S. Lee, S. F. R. TenHuisen, P. Zhou, S. Park, H. Kim, J.-K. Kim, H.-D. Kim, M. Kim, S.-Y. Park, P. Abbamonte, B. J. Kim, G. D. Gu, Y. Wang, and M. Mitrano, Phys. Rev. X 12, 011013 (2022)

    work page 2022

  13. [13]

    Fausti, R

    D. Fausti, R. I. Tobey, N. Dean, S. Kaiser, A. Di- enst, M. C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Science 331, 189 (2011), https://www.science.org/doi/pdf/10.1126/science.1197294. 17 FIG. 16. Comparison between the full expression Eq. 4 and the approximation Eq. 6 for the dynamical charge response of a 4 rung ladder using exact d...

    work page doi:10.1126/science.1197294 2011

  14. [14]

    Mitrano, A

    M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Ricc` o, S. R. Clark, D. Jaksch, and A. Cavalleri, Nature530, 461 (2016)

    work page 2016

  15. [15]

    J.-S. Caux, R. Hagemans, and J. M. Maillet, Journal of Statistical Mechanics: Theory and Experiment 2005, P09003 (2005)

    work page 2005

  16. [16]

    A. J. A. James, F. H. L. Essler, and R. M. Konik, Phys. Rev. B 78, 094411 (2008)

    work page 2008

  17. [17]

    W. D. Goetze, U. Karahasanovic, and F. H. L. Essler, Phys. Rev. B 82, 104417 (2010)

    work page 2010

  18. [18]

    D. A. Tennant, B. Lake, A. J. A. James, F. H. L. Essler, S. Notbohm, H.-J. Mikeska, J. Fielden, P. K¨ ogerler, P. C. Canfield, and M. T. F. Telling, Phys. Rev. B 85, 014402 (2012)

    work page 2012

  19. [19]

    Y. Wang, M. Claassen, B. Moritz, and T. P. Devereaux, Phys. Rev. B 96, 235142 (2017)

    work page 2017

  20. [20]

    Kaneko, T

    T. Kaneko, T. Shirakawa, S. Sorella, and S. Yunoki, Phys. Rev. Lett. 122, 077002 (2019)

    work page 2019

  21. [21]

    Ejima, T

    S. Ejima, T. Kaneko, F. Lange, S. Yunoki, and H. Fehske, Phys. Rev. Res. 2, 032008 (2020)

    work page 2020

  22. [22]

    Ejima, F

    S. Ejima, F. Lange, and H. Fehske, The European Phys- ical Journal Special Topics 232, 3479 (2023)

    work page 2023

  23. [23]

    Murakami, S

    Y. Murakami, S. Takayoshi, T. Kaneko, Z. Sun, D. Goleˇ z, A. J. Millis, and P. Werner, Communications Physics 5, 23 (2022)

    work page 2022

  24. [24]

    Eckstein and P

    M. Eckstein and P. Werner, Scientific Reports 6, 21235 (2016)

    work page 2016

  25. [25]

    Murakami, D

    Y. Murakami, D. Goleˇ z, M. Eckstein, and P. Werner, Photo-induced nonequilibrium states in mott insulators (2023), arXiv:2310.05201 [cond-mat.str-el]

    work page arXiv 2023

  26. [26]

    Ren and R

    T. Ren and R. M. Konik, Ultrafast control of mag- netic correlations in a heisenberg spin ladder (2023), arXiv:2307.13914 [cond-mat.str-el]

    work page arXiv 2023

  27. [27]

    Giamarchi, Quantum Physics in One Dimension (Ox- ford University Press, 2003)

    T. Giamarchi, Quantum Physics in One Dimension (Ox- ford University Press, 2003)

    work page 2003

  28. [28]

    Noack, S

    R. Noack, S. White, and D. Scalapino, Physica C: Super- conductivity 270, 281 (1996)

    work page 1996

  29. [29]

    Yang and A

    C. Yang and A. E. Feiguin, Phys. Rev. B 99, 235117 (2019)

    work page 2019

  30. [30]

    A. J. A. James and R. M. Konik, ChainAMPS is a set of libraries and driver routines, designed to implement MPS algorithms for large systems of coupled chains, https: //github.com/andyjaj/chainamps

    work page

  31. [31]

    J. K. Freericks, H. R. Krishnamurthy, and T. Pruschke, Phys. Rev. Lett. 102, 136401 (2009)

    work page 2009

  32. [32]

    H. N. Phien, G. Vidal, and I. P. McCulloch, Phys. Rev. B 86, 245107 (2012)

    work page 2012

  33. [33]

    H. N. Phien, G. Vidal, and I. P. McCulloch, Phys. Rev. B 88, 035103 (2013)

    work page 2013

  34. [34]

    Milsted, J

    A. Milsted, J. Haegeman, T. J. Osborne, and F. Ver- straete, Phys. Rev. B 88, 155116 (2013)

    work page 2013

  35. [35]

    Zauner, M

    V. Zauner, M. Ganahl, H. G. Evertz, and T. Nishino, Journal of Physics: Condensed Matter 27, 425602 (2015)

    work page 2015

  36. [36]

    Fabrizio and A

    M. Fabrizio and A. Parola, Phys. Rev. Lett. 70, 226 (1993)

    work page 1993

  37. [37]

    Endres, R

    H. Endres, R. M. Noack, W. Hanke, D. Poilblanc, and D. J. Scalapino, Phys. Rev. B 53, 5530 (1996)

    work page 1996

  38. [38]

    9 and 10 is a consequence of the finite window used in the frequency Fourier trans- form

    The very small amount of negative spectral weight visible for two of the curves in Figs. 9 and 10 is a consequence of the finite window used in the frequency Fourier trans- form. This negative weight could be removed by using a larger time window at a significant computational cost

    work page

  39. [39]

    F. H. L. Essler and R. M. Konik, Phys. Rev. B78, 100403 (2008)

    work page 2008

  40. [40]

    D. L. Quintero-Castro, B. Lake, A. T. M. N. Islam, E. M. Wheeler, C. Balz, M. M˚ ansson, K. C. Rule, S. Gvasaliya, and A. Zheludev, Phys. Rev. Lett. 109, 127206 (2012)

    work page 2012

  41. [41]

    Villain, Physica B+C 79, 1 (1975)

    J. Villain, Physica B+C 79, 1 (1975)

    work page 1975

  42. [42]

    Nocera, F

    A. Nocera, F. H. L. Essler, and A. E. Feiguin, Phys. Rev. B 97, 045146 (2018)

    work page 2018