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arxiv: 2604.27051 · v1 · submitted 2026-04-29 · ❄️ cond-mat.str-el

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Local Current Algebra for the HK Universality Class

Yuting Bai , Philip W. Phillips
Authors on Pith no claims yet

Pith reviewed 2026-05-07 08:55 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Hatsugai-Kohmoto modelcurrent algebraaffine Lie algebraMott insulatordoped Mott insulatorcharge susceptibilitylocal currentsstrong interactions
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The pith

A Hamiltonian in local real-space currents obeying an su_1(2) affine Lie algebra removes non-locality from the Hatsugai-Kohmoto model.

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

The paper demonstrates that the Hatsugai-Kohmoto model for doped Mott insulators, previously criticized for non-locality in its fermionic formulation, can be rewritten as a local Hamiltonian using currents. These currents satisfy an su_1(2) affine Lie algebra, with the mapping established by the Bjorken-Johnson-Low prescription for anomalous commutators. The charge susceptibility calculated from this current Hamiltonian matches exactly the one obtained from the original fermionic fields. This equivalence shows that the model is local when expressed in real-space currents, even if non-local in electron operators, thereby strengthening its applicability to strong-correlation problems.

Core claim

We show that a Hamiltonian in terms of the local real-space currents obeying an su_1(2) affine Lie algebra eliminates the non-locality in the Hatsugai-Kohmoto model for a doped Mott insulator. We establish this local correspondence through the Bjorken-Johnson-Low prescription for anomalous commutators. With this result, we show that the charge susceptibility computed from the current Hamiltonian is identical to that with the elemental Fermionic fields. Consequently, the HK model is local in real space, though not in terms of the Fermionic fields, thereby eliminating the key criticism of this model and reinforcing the utility of current algebras for strong interactions.

What carries the argument

Local real-space currents obeying an su_1(2) affine Lie algebra, connected to the original fermionic HK Hamiltonian via the Bjorken-Johnson-Low prescription for anomalous commutators.

If this is right

  • The charge susceptibility from the current Hamiltonian is identical to the fermionic version.
  • The HK model qualifies as local when formulated with real-space currents rather than electrons.
  • This formulation removes the main objection to using the HK model for doped Mott insulators.
  • Current algebras become a practical tool for capturing strong interactions without non-local operators.

Where Pith is reading between the lines

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

  • The same current-algebra approach could re-express other models with apparent non-locality, such as certain t-J variants, as local theories.
  • Numerical or analytical methods that exploit the su_1(2) algebra structure might become feasible for computing dynamics in doped insulators.
  • Experiments measuring current correlations directly could distinguish HK-like physics from conventional Fermi-liquid descriptions.

Load-bearing premise

The Bjorken-Johnson-Low prescription for anomalous commutators maps the current algebra to the original fermionic HK model without altering its physics.

What would settle it

A mismatch between the current-algebra Hamiltonian and the fermionic HK model in any observable besides charge susceptibility, such as spin susceptibility or single-particle spectral function, would show the equivalence fails.

read the original abstract

We show that a Hamiltonian in terms of the local real-space currents obeying an $\mathfrak{su}_1(2)$ affine Lie algebra eliminates the non-locality in the Hatsugai-Kohmoto model for a doped Mott insulator. We establish this local correspondence through the Bjorken-Johnson-Low prescription for anomalous commutators. With this result, we show that the charge susceptibility computed from the current Hamiltonian is identical to that with the elemental Fermionic fields. Consequently, the HK model is local in real space, though not in terms of the Fermionic fields, thereby eliminating the key criticism of this model and reinforcing the utility of current algebras for strong interactions.

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 a Hamiltonian formulated in terms of local real-space currents obeying an su_1(2) affine Lie algebra removes the non-locality of the Hatsugai-Kohmoto (HK) model for a doped Mott insulator. This local correspondence is established via the Bjorken-Johnson-Low (BJL) prescription for anomalous commutators, and the authors show that the resulting charge susceptibility is identical to the one computed with the original fermionic fields, thereby concluding that the HK model is local in real space when expressed via currents.

Significance. If the equivalence is rigorously established, the result would be significant for studies of strongly correlated systems, as it offers a concrete route to address the non-locality criticism of the HK model using current-algebra techniques. The explicit verification that charge susceptibilities match provides a useful, falsifiable check and underscores the potential of affine Lie algebras for capturing strong-interaction physics without sacrificing locality in real space.

major comments (2)
  1. [§3] §3 (BJL derivation of the current Hamiltonian): The central claim of physical equivalence and elimination of non-locality rests on the BJL prescription recovering the exact momentum-diagonal fermionic bilinears of the HK interaction. The manuscript verifies this only by matching the charge susceptibility; it does not explicitly confirm that the full set of equal-time commutators or the operator algebra is preserved without regularization artifacts or omitted terms.
  2. [§5] §5 (Conclusions and universality claim): The assertion that the HK model is thereby 'local in real space' is load-bearing for the paper's main result, yet it is supported solely by the susceptibility identity. Additional evidence, such as matching of the single-particle Green's function or the ground-state energy, is needed to establish that the current-algebra Hamiltonian reproduces the full spectrum and dynamics rather than a single two-point function.
minor comments (2)
  1. [Abstract] The notation for the affine Lie algebra (su_1(2) vs. fraktur form) should be made consistent between the abstract and the body of the text.
  2. [§2] A brief table or explicit list comparing the key operators and their commutation relations in the fermionic and current formulations would improve clarity of the mapping.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for providing constructive comments that help clarify the scope of our results. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (BJL derivation of the current Hamiltonian): The central claim of physical equivalence and elimination of non-locality rests on the BJL prescription recovering the exact momentum-diagonal fermionic bilinears of the HK interaction. The manuscript verifies this only by matching the charge susceptibility; it does not explicitly confirm that the full set of equal-time commutators or the operator algebra is preserved without regularization artifacts or omitted terms.

    Authors: We agree that the manuscript's primary check is the charge susceptibility. The BJL prescription is applied to derive the commutators that define the local current operators, and the Hamiltonian is written directly in terms of these currents to reproduce the HK interaction. By this construction, the equal-time commutators are those of the su_1(2) affine algebra, matching the fermionic case without omitted terms or artifacts, as the currents are defined locally in real space. The susceptibility identity serves as an independent verification of the physical equivalence. To address the referee's concern, we will include in the revised manuscript an explicit discussion in §3 of how the algebra is preserved by the BJL-derived Hamiltonian. revision: partial

  2. Referee: [§5] §5 (Conclusions and universality claim): The assertion that the HK model is thereby 'local in real space' is load-bearing for the paper's main result, yet it is supported solely by the susceptibility identity. Additional evidence, such as matching of the single-particle Green's function or the ground-state energy, is needed to establish that the current-algebra Hamiltonian reproduces the full spectrum and dynamics rather than a single two-point function.

    Authors: The locality in real space is achieved because the current Hamiltonian uses strictly local operators in position space, in contrast to the non-local fermionic bilinears in the original HK model. The identical charge susceptibility demonstrates that this local formulation captures the same charge dynamics. While we acknowledge that this does not constitute a proof of equivalence for all observables such as the single-particle Green's function or ground-state energy, our focus is on establishing a local current-algebra representation for the HK universality class. In the revised conclusions, we will clarify the extent of the equivalence shown and indicate that matching additional quantities would be a natural extension. revision: partial

Circularity Check

1 steps flagged

Charge susceptibility identity follows tautologically once BJL equivalence is asserted

specific steps
  1. self definitional [Abstract]
    "We establish this local correspondence through the Bjorken-Johnson-Low prescription for anomalous commutators. With this result, we show that the charge susceptibility computed from the current Hamiltonian is identical to that with the elemental Fermionic fields."

    The BJL step is used to declare the current-algebra Hamiltonian equivalent to the fermionic HK model. Once that equivalence is granted, the susceptibility (a physical observable of the model) is necessarily identical; reporting the match as a separate derived result is therefore self-referential rather than an independent check of the claimed locality.

full rationale

The paper asserts a local current-algebra Hamiltonian via the BJL prescription that maps exactly onto the original fermionic HK model. It then presents the identity of charge susceptibilities as an independent computed result. Because the two Hamiltonians are defined to be physically equivalent by that mapping, any two-point function (including susceptibility) must match by construction; the 'show that' step therefore reduces to the input equivalence claim rather than providing new verification.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the su(2)_1 current algebra and the applicability of the BJL prescription; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Currents obey an su_1(2) affine Lie algebra
    Invoked to construct the local Hamiltonian that eliminates non-locality.
  • domain assumption Bjorken-Johnson-Low prescription correctly handles anomalous commutators for this model
    Used to establish the local correspondence between current and fermionic formulations.

pith-pipeline@v0.9.0 · 5400 in / 1295 out tokens · 40120 ms · 2026-05-07T08:55:45.357461+00:00 · methodology

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Reference graph

Works this paper leans on

35 extracted references · 5 canonical work pages · 1 internal anchor

  1. [1]

    A field theory of currents.Phys

    Hirotaka Sugawara. A field theory of currents.Phys. Rev., 170:1659–1662, Jun 1968

    1968

  2. [2]

    Tomonaga

    S. Tomonaga. Remarks on Bloch’s Method of Sound Waves applied to Many-Fermion Problems.Prog. Theor. Phys., 5:544– 569, 1950

    1950

  3. [3]

    Exact solution of a many- fermion system and its associated boson field.Journal of Math- ematical physics, 6(2):304–312, 1965

    Daniel C Mattis and Elliott H Lieb. Exact solution of a many- fermion system and its associated boson field.Journal of Math- ematical physics, 6(2):304–312, 1965

    1965

  4. [4]

    ’luttinger liquid theory’ of one-dimensional quantum fluids

    F D M Haldane. ’luttinger liquid theory’ of one-dimensional quantum fluids. i. properties of the luttinger model and their ex- tension to the general 1d interacting spinless fermi gas.Journal of Physics C: Solid State Physics, 14(19):2585, jul 1981

    1981

  5. [5]

    Quantum sine-gordon equation as the massive thirring model.Phys

    Sidney Coleman. Quantum sine-gordon equation as the massive thirring model.Phys. Rev. D, 11:2088–2097, Apr 1975

    2088

  6. [6]

    Delacr ´etaz, Yi-Hsien Du, Umang Mehta, and Dam Thanh Son

    Luca V . Delacr ´etaz, Yi-Hsien Du, Umang Mehta, and Dam Thanh Son. Nonlinear bosonization of fermi surfaces: The method of coadjoint orbits.Phys. Rev. Res., 4:033131, Aug 2022

    2022

  7. [7]

    Cambridge University Press, 2005

    Fabian HL Essler, Holger Frahm, Frank G ¨ohmann, Andreas Kl¨umper, and Vladimir E Korepin.The one-dimensional Hub- bard model. Cambridge University Press, 2005

    2005

  8. [9]

    Phillips

    Gaurav Tenkila, Jinchao Zhao, and Philip W. Phillips. Dynam- ical Spectral Weight Transfer in the Orbital HK Model.arXiv e-prints, page arXiv:2406.17846, June 2024

    work page arXiv 2024

  9. [11]

    Huang, and Philip W

    Jinchao Zhao, Luke Yeo, Edwin W. Huang, and Philip W. Phillips. Thermodynamics of an exactly solvable model for superconductivity in a doped mott insulator.Phys. Rev. B, 105:184509, May 2022

    2022

  10. [12]

    Phillips, Luke Yeo, and Edwin W

    Philip W. Phillips, Luke Yeo, and Edwin W. Huang. Exact the- ory for superconductivity in a doped mott insulator.Nature Physics, 16(12):1175–1180, jul 2020

    2020

  11. [14]

    Hackner, Dhruv Kush, Derek Pan, and Philip W

    Peizhi Mai, Jinchao Zhao, Gaurav Tenkila, Nico A. Hackner, Dhruv Kush, Derek Pan, and Philip W. Phillips. Twisting the hubbard model into the momentum-mixing hatsugai–kohmoto model.Nature Physics, 22(1):81–87, 2026

    2026

  12. [15]

    Huang, Dhruv Kush, Barry Bradlyn, and Philip W

    Yuhao Ma, Jinchao Zhao, Edwin W. Huang, Dhruv Kush, Barry Bradlyn, and Philip W. Phillips. Charge susceptibility and kubo response in hatsugai-kohmoto-related models.Phys. Rev. B, 112:045109, Jul 2025

    2025

  13. [16]

    Phillips

    Jinchao Zhao, Gabriele La Nave, and Philip W. Phillips. Proof of a stable fixed point for strongly correlated electron matter. Phys. Rev. B, 108:165135, Oct 2023

    2023

  14. [17]

    Failure of topological invariants in strongly correlated matter

    Jinchao Zhao, Peizhi Mai, Barry Bradlyn, and Philip Phillips. Failure of topological invariants in strongly correlated matter. Physical Review Letters, 131(10), sep 2023

    2023

  15. [18]

    Phillips.Z 2 Universality of the Mott Transition.arXiv e-prints, page arXiv:2510.25845, October 2025

    Jinchao Zhao, Peizhi Mai, Gaurav Tenkila, and Philip W. Phillips.Z 2 Universality of the Mott Transition.arXiv e-prints, page arXiv:2510.25845, October 2025

    work page arXiv 2025

  16. [19]

    Feldman, and Philip W

    Peizhi Mai, Jinchao Zhao, Benjamin E. Feldman, and Philip W. Phillips. 1/4 is the new 1/2 when topology is intertwined with mottness.Nature Communications, 14(1):5999, 2023

    2023

  17. [20]

    Twisting the hubbard model into the momentum-mixing hatsugai–kohmoto model.Nature Physics, 22(1):81–87, 2026

    Peizhi Mai, Jinchao Zhao, Gaurav Tenkila, Nico A Hackner, Dhruv Kush, Derek Pan, and Philip W Phillips. Twisting the hubbard model into the momentum-mixing hatsugai–kohmoto model.Nature Physics, 22(1):81–87, 2026

    2026

  18. [21]

    Huang, Gabriele La Nave, and Philip W

    Edwin W. Huang, Gabriele La Nave, and Philip W. Phillips. Discrete symmetry breaking defines the mott quartic fixed point.Nature Physics, 18(5):511–516, mar 2022

    2022

  19. [22]

    Proof that momentum mix- ing hatsugai kohmoto equals the twisted hubbard model.arXiv preprint arXiv:2512.03148, 2025

    Yuting Bai and Philip W Phillips. Proof that momentum mix- ing hatsugai kohmoto equals the twisted hubbard model.arXiv preprint arXiv:2512.03148, 2025

    work page arXiv 2025

  20. [23]

    mixing solves the mott problem.Nature Physics, 22:17–18, 2026

    Philip W Phillips and Gaurav Tenkila. mixing solves the mott problem.Nature Physics, 22:17–18, 2026

    2026

  21. [24]

    Ground state sta- bility, symmetry, and degeneracy in mott insulators with long- range interactions.Phys

    Dmitry Manning-Coe and Barry Bradlyn. Ground state sta- bility, symmetry, and degeneracy in mott insulators with long- range interactions.Phys. Rev. B, 108:165136, Oct 2023

    2023

  22. [25]

    Decomposing momentum scales in the Hubbard Model: From Hatsugai-Kohmoto to Aubry-Andr\'e

    Dmitry Manning-Coe and Barry Bradlyn. Decomposing mo- mentum scales in the hubbard model: From hatsugai-kohmoto to aubry-andr\’e.arXiv preprint arXiv:2604.06588, 2026. 6

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  23. [26]

    Solving the su (n) orbital hatsugai-kohmoto model.Physical Review A, 111(6):063316, 2025

    Nico A Hackner, Peizhi Mai, and Philip W Phillips. Solving the su (n) orbital hatsugai-kohmoto model.Physical Review A, 111(6):063316, 2025

    2025

  24. [27]

    Anderson and F

    Philip W. Anderson and F. Duncan M. Haldane. The symme- tries of fermion fluids at low dimensions.Journal of Statistical Physics, 103(3):425–428, 2001

    2001

  25. [28]

    Current algebras in a simple model

    K Johnson and FE Low. Current algebras in a simple model. Progress of Theoretical Physics Supplement, 37:74–93, 1966

    1966

  26. [29]

    Applications of the chiral u (6)⊗u (6) alge- bra of current densities.Physical Review, 148(4):1467, 1966

    James D Bjorken. Applications of the chiral u (6)⊗u (6) alge- bra of current densities.Physical Review, 148(4):1467, 1966

    1966

  27. [30]

    Springer Science & Business Media, 2012

    Philippe Francesco, Pierre Mathieu, and David S ´en´echal.Con- formal field theory. Springer Science & Business Media, 2012

    2012

  28. [31]

    A field theory of currents.Physical Review, 170(5):1659, 1968

    Hirotaka Sugawara. A field theory of currents.Physical Review, 170(5):1659, 1968

    1968

  29. [32]

    Exactly solvable model of correlated lattice electrons in any dimensions.Journal of the Physical Society of Japan, 61(6):2056–2069, 1992

    Yasuhiro Hatsugai and Mahito Kohmoto. Exactly solvable model of correlated lattice electrons in any dimensions.Journal of the Physical Society of Japan, 61(6):2056–2069, 1992

    2056

  30. [33]

    Princeton University Press, 2014

    Sam Treiman and Roman Jackiw.Current algebra and anoma- lies. Princeton University Press, 2014

    2014

  31. [34]

    M. B. J. Meinders, H. Eskes, and G. A. Sawatzky. Spectral- weight transfer: Breakdown of low-energy-scale sum rules in correlated systems.Phys. Rev. B, 48(6):3916–3926, Aug 1993

    1993

  32. [35]

    Eskes, M

    H. Eskes, M. B. J. Meinders, and G. A. Sawatzky. Anomalous transfer of spectral weight in doped strongly correlated systems. Phys. Rev. Lett., 67:1035–1038, Aug 1991

    1991

  33. [36]

    Born-oppenheimer approximation and the ori- gin of wess-zumino terms: Some quantum-mechanical exam- ples.Phys

    Michael Stone. Born-oppenheimer approximation and the ori- gin of wess-zumino terms: Some quantum-mechanical exam- ples.Phys. Rev. D, 33:1191–1194, Feb 1986

    1986

  34. [37]

    New ap- proach to strong correlation: Twisting hubbard into the orbital hatsugai-kohmoto model.arXiv preprint arXiv:2401.08746, 2024

    Peizhi Mai, Jinchao Zhao, Gaurav Tenkila, Nico A Hackner, Dhruv Kush, Derek Pan, and Philip W Phillips. New ap- proach to strong correlation: Twisting hubbard into the orbital hatsugai-kohmoto model.arXiv preprint arXiv:2401.08746, 2024

    work page arXiv 2024

  35. [38]

    Phillips

    Gabriele La Nave, Jinchao Zhao, and Philip W. Phillips. Lut- tinger count is the homotopy not the physical charge: General- ized anomalies characterize non-fermi liquids.Phys. Rev. Lett., 135:246501, Dec 2025. A. Derivation of BJL Prescription Here we present the proof of the BJL prescription [28, 29, 33]. For two arbitrary states,|a⟩,|b⟩, the BJL prescri...

    2025