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REVIEW 3 major objections 4 minor 51 references

Emergence of Topological Non-Fermi Liquid Phases in a Modified Su-Schrieffer-Heeger Chain with Long-Range Interactions

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Pith's one-line read Adding momentum-local Hatsugai-Kohmoto interactions to the SSH chain yields exactly solvable non-Fermi liquid ground states, with a many-body Zak phase of $2\pi$ for $v<w$ and $0$ for $v>w$, identified as topological and trivial phases.

desk verdict Clean exact diagonalization of an SSH-HK chain, but the claimed topological NFL marker is vacuous because the Zak phase is defined modulo 2π. read the letter →

arxiv 2501.19023 v2 pith:RTN2FGKH submitted 2025-01-31 cond-mat.str-el quant-ph

Sepide Mohamadi , Jahanfar Abouie This is my paper · ORCID
classification cond-mat.str-elquant-ph
keywords Su-Schrieffer-HeegerchainHatsugai-Kohmotointeractionnon-Fermiliquidmany-bodyZakphasetopologicalphasesexactdiagonalizationspectralfunction
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

The paper studies a one-dimensional Su-Schrieffer-Heeger (SSH) chain--a dimerized hopping model--with long-range Hatsugai-Kohmoto (HK) interactions that are local in momentum space, which makes the interacting Hamiltonian exactly solvable. It claims that the ground state is a non-Fermi liquid, meaning ordinary quasiparticle descriptions fail, across almost the whole $v$--$U$ phase diagram, with only a single Fermi-liquid line as exception. To label these non-Fermi liquid phases topologically it computes a many-body Zak phase, obtaining $Z_{mb}=2\pi$ for $vw$ in the two-particle sector, and identifies the $2\pi$ state as a topological non-Fermi liquid that carries electronic polarization $P=e$. This would be an exactly solvable one-dimensional example where strong correlations and topological order coexist, with potential relevance to correlated metals and high-temperature superconductivity.

What carries the argument

The central object is the momentum-space Bloch Hamiltonian $H_k$ of the SSH-HK model, whose interaction term is diagonal in $k$ and conserves particle number, so the 16-state Hilbert space splits into $0$-, $1$-, $2$-, $3$-, and $4$-particle sectors. The load-bearing identity is the many-body Zak phase $Z_{mb}=i\int_0^{2\pi}dk\,\langle\Psi_k(1)|\partial_k|\Psi_k(1)\rangle$, evaluated on the exact ground state. Because the assumed $n=2$ ground state carries the phase factor $e^{-2i\phi_k}$, the integral collapses to $\oint d\phi_k=\Delta\phi_k$, giving $2\pi$ for $v<1$ and $0$ for $v>1$; a degenerate-sector version of the same formula treats the $n=1$ region. This geometric-phase machinery converts the exact eigenstates into a statement about topology and polarization.

What would settle it

Diagonalize the per-$k$ Hamiltonian at $k=\pi$ for $w=1$, $U=0.5$, and $v=0.75$: the one-particle energy $-|v-w|=-0.25$ lies below the assumed two-particle energy $U-2|v-w|=0$, so the ground state is not $|\Psi_k^{(2)}\rangle_5^-$ and Eq. (21) does not give the ground-state Zak phase at that point. Scanning $v$ and $U$ in this way defines the true boundary of the $n=2$ yellow region and determines whether a $2\pi$ many-body Zak phase exists anywhere in it.

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Extended reading notes

Core claim

Within the exactly solvable SSH-HK model, the authors show that the lowest-energy state at each momentum $k$ can be obtained by diagonalizing a 16-state Bloch Hamiltonian that factorizes into particle-number sectors. They find that the ground state is a non-Fermi liquid because the Luttinger integral does not equal the particle density except on one isolated line in the $v$--$U$ plane. For the $n=2$ region they take the ground state to be the nondegenerate dispersive two-particle state $|\Psi_k^{(2)}\rangle_5^-$ with energy $U-2|\epsilon_k|$, and from it they compute the many-body Zak phase $Z_{mb}=i\int dk\,\langle\Psi_k(1)|\partial_k|\Psi_k(1)\rangle$, obtaining $Z_{mb}=2\pi$ for $v<1$ and $0$ for $v>1$ (with $w=1$). They call the $2\pi$ phase a topological non-Fermi liquid and the $0$ phase trivial, and they argue that through $P_{mb}=eZ_{mb}/2\pi$ the $2\pi$ phase carries one electron's worth of polarization, in direct analogy with the noninteracting SSH chain.

Load-bearing premise

Everything about the 'topological' label in the $n=2$ region rests on the assumption that throughout that region the lowest state at every momentum $k$ is the nondegenerate two-particle state with energy $U-2|\epsilon_k|$; wherever that state is not the lowest, the many-body Zak phase computed from it is not the ground-state phase.

Editorial extensions

If this is right

  • If the $2\pi$ many-body Zak phase counts as topological, the SSH-HK chain is an exactly solvable one-dimensional non-Fermi liquid with quantized polarization $P=e$, matching the noninteracting SSH chain.
  • The model shows that non-Fermi liquid behavior, diagnosed by a Luttinger-volume mismatch, can coexist with sharp delta-function spectral peaks instead of broadened quasiparticles.
  • The $v$--$U$ phase diagram is dominated by NFL phases with particle densities $n=1$, $1<n<2$, and $n=2$, separated by a single Fermi-liquid line; adding a chemical potential extends the diagram to $n<1$ and produces Lifshitz transitions.
  • For $v<1$, the topological NFL labeling survives the addition of a chemical potential for the $n=1$ and $n=2$ sectors, while fractional- and zero-density phases are trivial; for $v>1$ all phases are trivial.

Reading between the lines

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

  • Because a Zak phase is only defined modulo $2\pi$, the values $2\pi$ and $0$ label the same geometric phase; distinguishing a topological from a trivial NFL in this model therefore requires an additional invariant, such as an edge-mode count or a quantized response, rather than the winding number alone.
  • The $n=2$ calculation silently assumes $U<|v-w|$ so that the dispersive two-particle state is lowest at every $k$. Scanning the per-$k$ ground state across the Brillouin zone for $U>|v-w|$ would map the true boundary of the yellow region and show whether any $2\pi$ phase survives there.
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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 / 4 minor

Summary. The paper studies a one-dimensional Su-Schrieffer-Heeger chain with Hatsugai-Kohmoto interactions, exactly diagonalizes the Bloch Hamiltonian in each particle-number sector, and uses the resulting eigenstates to compute ground-state densities, Luttinger integrals, many-body Zak phases, spectral functions, and density of states. The central claim is that the ground state supports non-Fermi liquid phases that are topologically distinct, with many-body Zak phases of 2π and 0 marking topological and trivial NFL phases, respectively.

Significance. The exact solvability of the SSH-HK model is a genuine strength: the block-diagonalization, closed-form eigenstates, phase diagram, and spectral functions are derived without numerical fitting and provide a concrete playground for studying interaction-induced NFL behavior. If the topological classification were correct, the paper would offer a rare exactly solvable example of a topological non-Fermi liquid. However, the central topological claim is invalid as stated, because the proposed Zak-phase distinction is empty modulo 2π, and the n=2 ground state used for the topological calculation is not the true ground state over a substantial parameter region.

major comments (3)
  1. [Sec. IV A, Eqs. (20)–(21)] The many-body Zak phase defined in Eq. (20) is a U(1) Berry phase over a closed Brillouin zone and is defined only modulo 2π. A k-dependent gauge transformation |Ψ_k⟩ → e^{iα_k}|Ψ_k⟩ with α_{2π} − α_0 = 2π changes Z_mb by 2π without changing any physical state, so Z_mb = 2π and Z_mb = 0 are the same equivalence class. Equation (21) therefore cannot distinguish a 'topological NFL' from a 'trivial NFL.' This is not a semantic quibble: Eq. (32) gives P = e for Z_mb = 2π and P = 0 for Z_mb = 0, but macroscopic polarization is likewise defined modulo e, so the two predictions are physically identical. For comparison, the noninteracting SSH topological phase is characterized by a Zak phase of π, not 2π, and the factor of 2 accumulated in Eq. (23) lands exactly on the trivial class 0 mod 2π. If the intended invariant is the integer winding number (1/2π)∮ dφ_k, that is a different quantity and must be defined and used as such.
  2. [Sec. IV A, text after Eq. (21)] The calculation for the n=2 yellow region assumes that the nondegenerate state |Ψ^(2)_k⟩₅⁻ with energy U − 2|ϵ_k| is the ground state at every k. This is false when U > 2|v−w|: near the Brillouin-zone edge, the zero-energy flat-band states |1010⟩ and |0101⟩ from the two-particle block (Eq. (9)) are lower in energy than U − 2|ϵ_k|, and the 0-particle vacuum at energy zero also competes. In that parameter regime the ground state is not the nondegenerate state used in Eq. (21), and the many-body Zak phase is not the value quoted. The paper provides no analysis of this crossover, which affects a large part of the n=2 region of the phase diagram.
  3. [Sec. V, Eqs. (33)–(34)] The spectral functions are presented as if the ground state in the n=1 and n=2 sectors is a single nondegenerate eigenstate. In the n=1 sector the ground state is doubly degenerate, and in the n=2 sector the flat-band degeneracy invalidates the single-state expression whenever U > 2|v−w|. The Green's function in Eq. (19) already includes a sum over degenerate ground states, but the explicit spectral formulas in Eqs. (33)–(34) do not appear to average over the correct ground-state manifold. The quasiparticle interpretation of the delta-function peaks is therefore not established in the parameter regions where the assumed ground state is not the true one.
minor comments (4)
  1. [Introduction] There is an unresolved citation placeholder "[ ? ]" in the sentence about n-dimensional SSH structures; this needs to be replaced by the intended reference.
  2. [Fig. 2 caption] The caption does not label the two degenerate zero-energy flat-band eigenstates of the two-particle sector, even though these states are essential to determining the ground state in the n=2 region.
  3. [Throughout] Several typographical errors remain, including "chemial" (Sec. VI heading), "propreties" (Sec. VII), "regardaing" (Sec. IV B), and "Hamiltonain" (before Eq. (6)). These should be corrected in a revised version.
  4. [Sec. IV B, Eq. (32)] The statement that Z_mb = 2π gives P = e and hence charge polarization should be clarified: polarization is only defined modulo e, so this value is indistinguishable from P = 0. The text should state explicitly that the physical content is a Z_2 or integer-winding classification, not a distinction between 2π and 0 as Zak phases.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the exact-diagonalization derivation is self-contained, and the 2π-vs-0 Zak-phase distinction is a mathematical validity flaw rather than a circular argument.

full rationale

The paper's central derivations are self-contained. The SSH-HK Hamiltonian is exactly diagonalized in Sec. II, yielding closed-form eigenstates and eigenenergies. The Luttinger integrals in Eq. (18) and the ground-state densities in Eq. (17) are then computed from those same eigenstates; no parameter is fitted to a target result, and the NFL classification is a direct comparison rather than a circular prediction. The many-body Zak phase in Eq. (20) is likewise evaluated from the explicitly constructed ground states, not extracted from a fitted parameter, and the later polarization formula Eq. (32) is a direct proportionality to that phase. The serious problem with the topological claim is different: the Zak phase is defined only modulo 2π, so the claimed distinction between Z_mb = 2π and Z_mb = 0 in Eq. (21) is not a valid order parameter, since the two values represent the same equivalence class. That is a correctness and consistency defect in the topological labeling, not a case of the derivation reducing to its own inputs. The only self-citation, Ref. [8] by Ahmadi, Abouie, and Baeriswyl, appears in a survey paragraph about generalized SSH models and is not load-bearing for the Hamiltonian, exact solution, Luttinger analysis, or Zak-phase calculation. No ansatz or uniqueness theorem is imported from the authors' own prior work. Thus there is no significant circularity; the score is 1, reflecting only a minor non-load-bearing self-citation while the central derivations remain independent.

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

No parameters are fitted to external data; U, v, w, and mu are model parameters scanned to produce phase diagrams, so the free-parameter ledger is empty. The central claims rest on three assumptions listed above, the most fragile being the neglect of the flat-band ground states in the two-particle sector and the interpretation of 2 pi as distinct from 0.

assumptions (3)
  • domain assumption The Luttinger integral with Heaviside step function of Re G(k, omega=0) is a valid diagnostic for Fermi liquid vs non-Fermi liquid in this gapped 1D system.
    Sec. III defines I_a and I_b such that equality with density marks a Fermi liquid. At U=0, Re G_aa(k,0)=0 for all k, so Theta(0) is ambiguous; the paper does not discuss this.
  • domain assumption The many-body Zak phase is defined modulo 2 pi, but the paper treats 2 pi and 0 as distinct topological labels.
    Sec. IV A Eqs. (21)-(23) assign 'topological' to Z=2 pi and 'trivial' to Z=0; standard Zak phase theory (Refs. 39-40, cited by the paper) defines the phase modulo 2 pi, so this distinction requires an unstated branch choice.
  • ad hoc to paper In the n=2 yellow region the ground state is everywhere the nondegenerate state |Psi^(2)>_5^-.
    Sec. IV A states this without proof, but Eq. (9) contains zero-energy flat-band states |1010> and |0101> that become lower in energy near the zone edge when U>2|v-w|, making the ground state degenerate.

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Cite this review

Pith. "Pith review of Emergence of Topological Non-Fermi Liquid Phases in a Modified Su-Schrieffer-Heeger Chain with Long-Range Interactions." pith.science (2026). https://pith.science/paper/RTN2FGKH

@misc{pith2026250119023,
  author       = {Pith},
  title        = {Pith review of: Emergence of Topological Non-Fermi Liquid Phases in a Modified Su-Schrieffer-Heeger Chain with Long-Range Interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RTN2FGKH}},
  note         = {Machine review of arXiv:2501.19023}
}
abstract

In this study, we investigate the emergence of a topological non-Fermi liquid (NFL) phase in a modified Su-Schrieffer-Heeger (SSH) chain model subjected to long-range interactions characterized by the Hatsugai-Kohmoto (HK) model. While Fermi liquid theory has been instrumental in understanding low temperature properties of metals, it fails to account for the complex behaviors exhibited by strongly correlated systems, where interactions lead to emergent phenomena such as non-Fermi liquid behavior. Our analysis reveals that the SSH-HK model supports a rich ground state phase diagram, exhibiting distinct NFL phases marked by many body Zak phases of $2\pi$ and $0$, corresponding to topological and trivial NFL states, respectively. We demonstrate that the topological NFL state manifests unique electronic polarization characteristics akin to those in the non-interacting SSH model. Through exact diagonalization of the interacting SSH-HK Hamiltonian, we explore the spectral functions and density of states, revealing significant departures from traditional quasiparticle behavior in various particle number sectors. Our findings extend the understanding of topological non-Fermi liquids and their potential implications for high-temperature superconductivity and other correlated electron systems, highlighting the intricate interplay between topology and strong electron correlations.

Figures

Figures reproduced from arXiv: 2501.19023 by the authors.

Figure 1
Figure 1. FIG. 1. The schematic of a 1D SSH-HK model. The black [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Eigenenergies of the SSH-HK Hamiltonian for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Top: Ground state particle density [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Ground state particle densities [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Ground state phase diagram of the SSH-HK model. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Energy of excitations (left column) and DOS (right [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Energy of excitations (left column) and DOS (right [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The particle densities and Luttinger integrals as a [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Particle density ( [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. The ground state phase diagram of the SSH-HK [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

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Works this paper leans on

51 extracted references · 50 canonical work pages

  1. [1]

    When the interaction U is turned off, the particle density remains saturated at n = 2 regardless of the value of v (see the red line in Fig. 3). In this scenario, the ground state of the system is a tensor product of the degenerate ground states of H (2) k , denoted by |Ψ(2) k ⟩4. In these states, na = nb =

    work page

  2. [2]

    Consequently, each k state is, on average, fully occupied by a↑ and a↓, and b↑ and b↓ particles

    work page

  3. [3]

    When the interaction U is turned on, there is an interval around v = 1 where the particle density drops below 2 (see the green and blue curves in Fig. 3). Within this interval, near the k = 0 point, the ground state of the Hk is in the 2-particle sec- tor, given by the states |Ψ(2) k ⟩4. However, away from this point, level crossings occur at twok points ...

    work page

  4. [4]

    When intracell hopping is small, the ground state particle density is n = 1

    As U increases, the particle density exhibits differ- ent behaviors. When intracell hopping is small, the ground state particle density is n = 1. This density increases with v and eventually saturates at n = 2 for v > 1. In the region with n = 1, the ground state of the Hk is in the 1-particle sector, given by the state |Ψ(1) k ⟩ − 1,2. In this state, na ...

    work page 1960

  5. [5]

    The theory of a Fermi liquid,

    L. D. Landau, “The theory of a Fermi liquid,” Sov. Phys. JETP, vol. 3, no. 6, p. 920, 1957

    work page 1957

  6. [6]

    Non-Fermi- liquid behavior and d-wave superconductivity near the charge-density-wave quantum critical point,

    C. Castellani, C. Di Castro, and M. Grilli, “Non-Fermi- liquid behavior and d-wave superconductivity near the charge-density-wave quantum critical point,”Z. Phys. B- Condensed Matter, vol. 103, pp. 137–144, 1996

    work page 1996

  7. [7]

    Theoretical progress and material studies of heavy fermion superconductors,

    L. Yu, S. Yu-Tao, and Y. Yi-Feng, “Theoretical progress and material studies of heavy fermion superconductors,” Acta Phys. Sin., vol. 70, no. 1, 2021

    work page 2021

  8. [8]

    Non Fermi liquid be- havior in strongly correlated f-electron materials,

    M. Maple, C. Seaman, D. Gajewski, Y. Dalichaouch, V. Barbetta, M. De Andrade, H. Mook, H. Lukefahr, O. Bernal, and D. MacLaughlin, “Non Fermi liquid be- havior in strongly correlated f-electron materials,” Jour- nal of Low Temperature Physics, vol. 95, pp. 225–243, 1994

    work page 1994

Show all 51 references
  1. [9]

    Formation of a topological non-Fermi liquid in MnSi,

    R. Ritz, M. Halder, M. Wagner, C. Franz, A. Bauer, and C. Pfleiderer, “Formation of a topological non-Fermi liquid in MnSi,” Nature, vol. 497, no. 7448, pp. 231–234, 2013

    2013

  2. [10]

    Non- fermi-liquid and topological states with strong spin-orbit coupling,

    E.-G. Moon, C. Xu, Y. B. Kim, and L. Balents, “Non- fermi-liquid and topological states with strong spin-orbit coupling,” Physical Review Letters, vol. 111, no. 20, p. 206401, 2013

    2013

  3. [11]

    Analytic solution of the n-dimensional Su- Schrieffer-Heeger model,

    F. Liu, “Analytic solution of the n-dimensional Su- Schrieffer-Heeger model,” Physical Review B, vol. 108, no. 24, p. 245140, 2023

    2023

  4. [12]

    Topological and nontopological features of generalized Su-Schrieffer- Heeger models,

    N. Ahmadi, J. Abouie, and D. Baeriswyl, “Topological and nontopological features of generalized Su-Schrieffer- Heeger models,” Physical Review B, vol. 101, no. 19, p. 195117, 2020

    2020

  5. [13]

    Topological phases of gener- alized Su-Schrieffer-Heeger models,

    L. Li, Z. Xu, and S. Chen, “Topological phases of gener- alized Su-Schrieffer-Heeger models,” Physical Review B, vol. 89, no. 8, p. 085111, 2014

    2014

  6. [14]

    Chiral topological phases and fractional domain wall excitations in one-dimensional chains and wires,

    J. I. V¨ ayrynen and T. Ojanen, “Chiral topological phases and fractional domain wall excitations in one-dimensional chains and wires,” Physical Review Letters, vol. 107, no. 16, p. 166804, 2011

    2011

  7. [15]

    Topological phases, topological flat bands, and topological excitations in a one-dimensional dimerized lattice with spin-orbit coupling,

    Z. Yan and S. Wan, “Topological phases, topological flat bands, and topological excitations in a one-dimensional dimerized lattice with spin-orbit coupling,” Europhysics Letters, vol. 107, no. 4, p. 47007, 2014

    2014

  8. [16]

    Zeeman-field-induced nontrivial topological phases in a one-dimensional spin- orbit-coupled dimerized lattice,

    M. Bahari and M. V. Hosseini, “Zeeman-field-induced nontrivial topological phases in a one-dimensional spin- orbit-coupled dimerized lattice,” Physical Review B , vol. 94, no. 12, p. 125119, 2016

    2016

  9. [17]

    Theory of electron spin resonance in one- dimensional topological insulators with spin-orbit cou- plings: Detection of edge states,

    Y. Yao, M. Sato, T. Nakamura, N. Furukawa, and M. Oshikawa, “Theory of electron spin resonance in one- dimensional topological insulators with spin-orbit cou- plings: Detection of edge states,” Physical Review B, vol. 96, no. 20, p. 205424, 2017

    2017

  10. [18]

    Topological phases of a dimerized Fermi-hubbard model for semiconductor nano-lattices,

    N. H. Le, A. J. Fisher, N. J. Curson, and E. Ginossar, “Topological phases of a dimerized Fermi-hubbard model for semiconductor nano-lattices,” NPJ Quantum Infor- mation, vol. 6, no. 1, p. 24, 2020

    2020

  11. [19]

    Attractive Su-Schrieffer-Heeger-Hubbard model on a square lattice away from half-filling,

    B. Xing, C. Feng, R. Scalettar, G. G. Batrouni, and D. Poletti, “Attractive Su-Schrieffer-Heeger-Hubbard model on a square lattice away from half-filling,”Physical Review B, vol. 108, no. 16, p. L161103, 2023

    2023

  12. [20]

    Phase diagram of the Su-Schrieffer-Heeger- Hubbard model on a square lattice,

    C. Feng, B. Xing, D. Poletti, R. Scalettar, and G. Ba- trouni, “Phase diagram of the Su-Schrieffer-Heeger- Hubbard model on a square lattice,” Physical Review B, vol. 106, no. 8, p. L081114, 2022

    2022

  13. [21]

    Robustness of antiferro- magnetism in the Su-Schrieffer-Heeger Hubbard model,

    X. Cai, Z.-X. Li, and H. Yao, “Robustness of antiferro- magnetism in the Su-Schrieffer-Heeger Hubbard model,” 14 Physical Review B, vol. 106, no. 8, p. L081115, 2022

    2022

  14. [22]

    Exactly solvable model of correlated lattice electrons in any dimensions,

    Y. Hatsugai and M. Kohmoto, “Exactly solvable model of correlated lattice electrons in any dimensions,” Journal of the Physical Society of Japan, vol. 61, no. 6, pp. 2056– 2069, 1992

    1992

  15. [23]

    Topic review: Hatsugai-Kohmoto models: Exactly solvable playground for mottness and non-fermi liquid,

    M. Zhao, W.-W. Yang, and Y. Zhong, “Topic review: Hatsugai-Kohmoto models: Exactly solvable playground for mottness and non-fermi liquid,” arXiv preprint arXiv:2501.00388, 2024

    2024 arXiv

  16. [24]

    An introduction to the SYK model,

    V. Rosenhaus, “An introduction to the SYK model,” Journal of Physics A: Mathematical and Theoretical , vol. 52, no. 32, p. 323001, 2019

    2019

  17. [25]

    Remarks on the Sachdev-Ye-Kitaev model,

    J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Physical Review D, vol. 94, no. 10, p. 106002, 2016

    2016

  18. [26]

    Dilute magnetic moments in an exactly solv- able interacting host,

    C. Setty, “Dilute magnetic moments in an exactly solv- able interacting host,” arXiv preprint arXiv:2105.15205, 2021

    2021 arXiv

  19. [27]

    Exact theory for superconductivity in a doped mott insulator,

    P. W. Phillips, L. Yeo, and E. W. Huang, “Exact theory for superconductivity in a doped mott insulator,” Nature Physics, vol. 16, no. 12, pp. 1175–1180, 2020

    2020

  20. [28]

    Two- stage superconductivity in the Hatsugai-Kohomoto-BCS model,

    Y. Li, V. Mishra, Y. Zhou, and F.-C. Zhang, “Two- stage superconductivity in the Hatsugai-Kohomoto-BCS model,” New Journal of Physics , vol. 24, no. 10, p. 103019, 2022

    2022

  21. [29]

    Exactly solvable model of Fermi arcs and pseu- dogap,

    K. Yang, “Exactly solvable model of Fermi arcs and pseu- dogap,” Physical Review B, vol. 103, no. 2, p. 024529, 2021

    2021

  22. [30]

    Ther- modynamics of an exactly solvable model for supercon- ductivity in a doped mott insulator,

    J. Zhao, L. Yeo, E. W. Huang, and P. W. Phillips, “Ther- modynamics of an exactly solvable model for supercon- ductivity in a doped mott insulator,” Physical Review B, vol. 105, no. 18, p. 184509, 2022

    2022

  23. [31]

    Topological s-wave superconductors driven by electron correlation,

    H.-S. Zhu, Z. Li, Q. Han, and Z. Wang, “Topological s-wave superconductors driven by electron correlation,” Physical Review B, vol. 103, no. 2, p. 024514, 2021

    2021

  24. [32]

    Solvable periodic Anderson model with infinite-range Hatsugai-Kohmoto interaction: Ground- states and beyond,

    Y. Zhong, “Solvable periodic Anderson model with infinite-range Hatsugai-Kohmoto interaction: Ground- states and beyond,” Physical Review B, vol. 106, no. 15, p. 155119, 2022

    2022

  25. [33]

    A common thread: The pairing inter- action for unconventional superconductors,

    D. J. Scalapino, “A common thread: The pairing inter- action for unconventional superconductors,” Reviews of Modern Physics, vol. 84, no. 4, pp. 1383–1417, 2012

    2012

  26. [34]

    The resonating valence bond state in La2CuO4 and superconductivity,

    P. W. Anderson, “The resonating valence bond state in La2CuO4 and superconductivity,” Science, vol. 235, no. 4793, pp. 1196–1198, 1987

    1987

  27. [35]

    Solitons in polyacetylene,

    W.-P. Su, J. R. Schrieffer, and A. J. Heeger, “Solitons in polyacetylene,” Physical Review Letters, vol. 42, no. 25, p. 1698, 1979

    1979

  28. [36]

    Nonstandard symme- try classes in mesoscopic normal-superconducting hybrid structures,

    A. Altland and M. R. Zirnbauer, “Nonstandard symme- try classes in mesoscopic normal-superconducting hybrid structures,” Physical Review B, vol. 55, no. 2, p. 1142, 1997

    1997

  29. [37]

    Studies of polaron motion: Part i. the molecular-crystal model,

    T. Holstein, “Studies of polaron motion: Part i. the molecular-crystal model,” Annals of Physics , vol. 8, no. 3, pp. 325–342, 1959

    1959

  30. [38]

    Analyticity breaking and An- derson localization in incommensurate lattices,

    S. Aubry and G. Andr´ e, “Analyticity breaking and An- derson localization in incommensurate lattices,” Ann. Is- rael Phys. Soc, vol. 3, no. 133, p. 18, 1980

    1980

  31. [39]

    Elementary excitations of a lin- early conjugated diatomic polymer,

    M. Rice and E. Mele, “Elementary excitations of a lin- early conjugated diatomic polymer,” Physical Review Letters, vol. 49, no. 19, p. 1455, 1982

    1982

  32. [40]

    Coleman, Introduction to many-body physics

    P. Coleman, Introduction to many-body physics. Cam- bridge University Press, 2015

    2015

  33. [41]

    Unraveling of the fractional topological phase in one-dimensional flatbands with nontrivial topology,

    J. C. Budich and E. Ardonne, “Unraveling of the fractional topological phase in one-dimensional flatbands with nontrivial topology,” arXiv preprint arXiv:1304.4366, 2013

    2013 arXiv

  34. [42]

    Quantized hall conductance as a topological invariant,

    Q. Niu, D. J. Thouless, and Y.-S. Wu, “Quantized hall conductance as a topological invariant,” Physical Review B, vol. 31, no. 6, p. 3372, 1985

    1985

  35. [43]

    Macroscopic polarization in crystalline di- electrics: the geometric phase approach,

    R. Resta, “Macroscopic polarization in crystalline di- electrics: the geometric phase approach,” Reviews of Modern Physics, vol. 66, no. 3, p. 899, 1994

    1994

  36. [44]

    Theory of polariza- tion of crystalline solids,

    R. King-Smith and D. Vanderbilt, “Theory of polariza- tion of crystalline solids,” Physical Review B, vol. 47, no. 3, p. 1651, 1993

    1993

  37. [45]

    Topological phases of the interacting Su-Schrieffer-Heeger model: An analyti- cal study,

    E. Di Salvo, A. Moustaj, C. Xu, L. Fritz, A. Mitchell, C. M. Smith, and D. Schuricht, “Topological phases of the interacting Su-Schrieffer-Heeger model: An analyti- cal study,” Physical Review B, vol. 110, no. 16, p. 165145, 2024

    2024

  38. [46]

    Topo- logical edge states in the one-dimensional superlattice Bose-Hubbard model,

    F. Grusdt, M. H¨ oning, and M. Fleischhauer, “Topo- logical edge states in the one-dimensional superlattice Bose-Hubbard model,” Physical Review Letters, vol. 110, no. 26, p. 260405, 2013

    2013

  39. [47]

    Many-body effects on polariza- tion and dynamical charges in a partly covalent polar in- sulator,

    R. Resta and S. Sorella, “Many-body effects on polariza- tion and dynamical charges in a partly covalent polar in- sulator,” Physical Review Letters, vol. 74, no. 23, p. 4738, 1995

    1995

  40. [48]

    Macroscopic polarization as a geometric quantum phase: Many-body formulation,

    G. Ortiz and R. M. Martin, “Macroscopic polarization as a geometric quantum phase: Many-body formulation,” Physical Review B, vol. 49, no. 20, p. 14202, 1994

    1994

  41. [49]

    Sin- gular or non-Fermi liquids,

    C. M. Varma, Z. Nussinov, and W. Van Saarloos, “Sin- gular or non-Fermi liquids,” Physics Reports, vol. 361, no. 5-6, pp. 267–417, 2002

    2002

  42. [50]

    Density of states and spectral function of a superconductor out of a quantum- critical metal,

    S.-S. Zhang and A. V. Chubukov, “Density of states and spectral function of a superconductor out of a quantum- critical metal,” Physical Review Letters, vol. 131, no. 8, p. 086502, 2023

    2023

  43. [51]

    D. I. Khomskii, Basic aspects of the quantum theory of solids: order and elementary excitations. Cambridge uni- versity press, 2010

    2010

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.