arxiv: 2604.02426 · v1 · submitted 2026-04-02 · ❄️ cond-mat.str-el · cond-mat.supr-con

Recognition: 2 theorem links

· Lean Theorem

Transport and Temperature 1: Exact spectrum and resistivity for the one-dimensional infinite-U Hubbard model

Shuo Liu , Yuhao Ma , Hitesh J. Changlani , Philip W. Phillips , B. Andrei Bernevig

Authors on Pith no claims yet

Pith reviewed 2026-05-13 20:21 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.supr-con

keywords Hubbard modelinfinite U limitDrude weightresistivitylinear-in-Tone-dimensional systemscharge transportstrange metals

0 comments

The pith

In the dilute limit of the one-dimensional infinite-U Hubbard model, an exact energy spectrum yields a closed-form Drude weight whose regularization produces linear-in-T resistivity.

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

The authors construct an explicit energy spectrum for the infinite-U Hubbard chain with a fixed number of holes that goes beyond the standard Bethe-ansatz solution. Using this spectrum they obtain an exact analytical expression for the charge Drude weight that holds at arbitrary temperatures. The low-temperature expansion of this Drude weight contains a term linear in T. Regularizing the divergent zero-frequency conductivity converts the linear correction into a resistivity that rises linearly with temperature. This result supplies an analytic benchmark for the strange-metal behavior observed in two-dimensional correlated materials.

Core claim

In the infinite-U one-dimensional Hubbard model with fixed hole doping, the many-body energy spectrum admits an exact closed-form expression. The charge Drude weight extracted from this spectrum is given by a compact formula valid for all temperatures. Its low-temperature expansion features a linear-in-T correction; after the singular Drude delta function in the conductivity is regularized, this correction translates into a resistivity that is linear in temperature.

What carries the argument

The exact explicit energy spectrum of the dilute infinite-U Hubbard chain, from which the Drude weight is computed directly.

If this is right

The Drude weight is known analytically at any temperature.
A linear-in-T correction appears in the low-temperature Drude weight.
Regularization converts this into an effective linear-in-T resistivity.
This supplies an analytic window into strange-metal transport.

Where Pith is reading between the lines

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

Similar regularization procedures might apply to other integrable models with singular conductivities.
The result could be tested in ultracold-atom realizations of the 1D Hubbard model.
Extrapolation to higher dimensions may require checking whether the linear resistivity survives when interchain coupling is added.
The explicit spectrum might enable exact calculations of other transport coefficients such as thermal conductivity.

Load-bearing premise

The regularization of the singular Drude contribution produces a physically meaningful resistivity that remains valid outside the strict dilute limit and can be extrapolated toward two-dimensional strange-metal physics.

What would settle it

A numerical computation of the finite-temperature conductivity on finite chains, after applying the same regularization, should reproduce the predicted linear slope in resistivity versus temperature.

Figures

Figures reproduced from arXiv: 2604.02426 by B. Andrei Bernevig, Hitesh J. Changlani, Philip W. Phillips, Shuo Liu, Yuhao Ma.

**Figure 2.** Figure 2: FIG. 2. Resistivity [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

read the original abstract

Understanding charge transport in strongly correlated systems remains a central challenge in condensed matter physics, particularly in light of the ubiquitous linear-in-$T$ resistivity observed in strange metals across many platforms from bulk cuprates to twisted bilayer graphene. Here, we investigate charge transport in the one-dimensional Hubbard model in the infinite-interaction limit. Focusing on the dilute limit with a fixed number of doped holes, we first construct the exact \emph{and explicit - i.e. beyond Bethe ansatz} energy spectrum and then derive a closed-form analytical expression for the charge Drude weight at arbitrary temperatures. We further analyze the low-temperature scaling and identify a linear-in-$T$ correction to the Drude weight. Upon regularizing the singular Drude contribution to the DC conductivity, we find that this behavior corresponds to an effective linear-in-$T$ resistivity, which may provide analytical insight into the emergence of strange-metal transport in two-dimensional strongly correlated 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.

Desk Editor's Note private letter to a colleague

Explicit spectrum and closed-form Drude weight in the dilute 1D infinite-U Hubbard, but the linear-T resistivity rests on an under-specified regularization.

read the letter

The paper constructs an explicit energy spectrum for the infinite-U Hubbard chain in the dilute fixed-hole sector and uses it to obtain a closed-form expression for the charge Drude weight at arbitrary temperature. They also extract a linear-in-T correction to that weight at low T. After regularizing the delta-function Drude peak they report an effective resistivity that scales linearly with temperature. That is the central package. The spectrum construction is the part that stands out as new. Most prior work on this model relies on Bethe-ansatz thermodynamics or numerical diagonalization; writing the energies out explicitly lets them compute the Drude weight directly as a function of T without leaving it as a formal sum. That step is concrete and should be reproducible. The low-T expansion follows straightforwardly from the same spectrum. The regularization that turns the infinite DC conductivity into a finite linear-T resistivity is the softer element. The paper treats the smearing as a way to extract an effective resistivity that might inform strange-metal behavior, but it does not demonstrate that the procedure is uniquely determined by the model or that the linear-T result is stable under reasonable changes in the cutoff or broadening. The claim is therefore tied to the dilute limit they study and to the particular regularization chosen. This work is aimed at theorists who want exact benchmarks for transport in one-dimensional strongly correlated systems and at those looking for analytical templates for linear resistivity. The spectrum and Drude weight formulas are useful on their own even if the resistivity interpretation is taken as provisional. I would send the paper to peer review. The exact results are checkable and the regularization issue is the kind of point that referees familiar with Drude-weight calculations in integrable models can address directly.

Referee Report

2 major / 2 minor

Summary. The manuscript constructs an exact and explicit energy spectrum (beyond Bethe ansatz) for the one-dimensional infinite-U Hubbard model in the dilute limit with a fixed number of doped holes. From this spectrum it derives a closed-form expression for the charge Drude weight D(T) at arbitrary temperatures, identifies a linear-in-T correction in the low-T expansion, and, after regularizing the singular Drude delta-function contribution to the DC conductivity, obtains an effective linear-in-T resistivity that is proposed to illuminate strange-metal transport in two dimensions.

Significance. A rigorously derived closed-form Drude weight for this solvable limit would constitute a valuable analytical benchmark for charge transport in strongly correlated 1D systems. The explicit spectrum construction and the resulting D(T) are strengths if they are shown to be free of hidden parameters or reductions. The regularization step that converts the infinite Drude weight into a finite linear-T resistivity is the most consequential claim; if it can be placed on a unique, model-intrinsic footing that survives relaxation of the dilute limit, the work would offer concrete insight into the microscopic origin of linear-T resistivity.

major comments (2)

[regularization and conductivity section] The regularization procedure that converts the singular Drude peak into a finite resistivity is load-bearing for the central claim of linear-in-T behavior. The manuscript must specify the precise regularization (broadening, cutoff, or effective scattering rate) and demonstrate that the linear-T coefficient is independent of the regularization scheme while preserving the low-T expansion of D(T) derived from the spectrum.
[spectrum construction section] The assertion that the spectrum is 'explicit and beyond Bethe ansatz' requires a direct comparison, in the dilute fixed-hole sector, with the known Bethe-ansatz solution for the infinite-U Hubbard chain to establish novelty or equivalence; without this, the claim that the closed-form D(T) is new cannot be assessed.

minor comments (2)

[abstract] Clarify in the abstract and introduction whether the linear-T resistivity is obtained only in the strict dilute limit or is claimed to remain valid when hole density is increased.
Ensure all symbols in the closed-form expression for D(T) are defined before first use and that the low-T expansion is written with explicit coefficients.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive feedback. We address each major comment below and indicate the revisions we will implement.

read point-by-point responses

Referee: [regularization and conductivity section] The regularization procedure that converts the singular Drude peak into a finite resistivity is load-bearing for the central claim of linear-in-T behavior. The manuscript must specify the precise regularization (broadening, cutoff, or effective scattering rate) and demonstrate that the linear-T coefficient is independent of the regularization scheme while preserving the low-T expansion of D(T) derived from the spectrum.

Authors: We agree that the regularization requires explicit specification. In the revised manuscript we will define it as a Lorentzian broadening of width η applied to the frequency-dependent conductivity, with the DC limit taken after the thermodynamic limit but with η kept finite until the final step. We will show analytically that the linear-in-T coefficient extracted from the regularized resistivity is independent of η for sufficiently small η, because the singular Drude contribution is subtracted in a manner that exactly matches the low-T expansion of the closed-form D(T) obtained from the spectrum. revision: yes
Referee: [spectrum construction section] The assertion that the spectrum is 'explicit and beyond Bethe ansatz' requires a direct comparison, in the dilute fixed-hole sector, with the known Bethe-ansatz solution for the infinite-U Hubbard chain to establish novelty or equivalence; without this, the claim that the closed-form D(T) is new cannot be assessed.

Authors: We thank the referee for this request. Our construction yields an explicit combinatorial formula for the energies in the dilute fixed-hole sector that does not involve solving the Bethe equations. In the revision we will add a direct comparison for small systems (e.g., two holes on chains of length L = 10–20), demonstrating that the energies coincide with those obtained from the known Bethe-ansatz solution in the U = ∞ limit, while underscoring that the explicit closed-form character of our spectrum is what permits the closed-form D(T) at arbitrary temperature. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation proceeds from constructed spectrum to explicit Drude weight formula without reduction to inputs by definition

full rationale

The paper first constructs an explicit energy spectrum for the dilute fixed-hole sector of the infinite-U Hubbard model and then derives a closed-form analytical expression for the charge Drude weight directly from that spectrum. This step is presented as a direct computation at arbitrary temperatures, with an additional low-T expansion identified separately. The regularization of the singular Drude delta function to obtain an effective linear-in-T resistivity is an interpretive modeling choice applied after the exact result, not a step that redefines or fits the input spectrum to force the output. No self-citations, fitted parameters renamed as predictions, or ansatze smuggled via prior work are indicated as load-bearing in the derivation chain. The central claims therefore remain self-contained against the constructed spectrum.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the infinite-U limit forbidding double occupancy and on the dilute fixed-hole-number regime; both are standard domain assumptions with no free parameters or new entities introduced in the abstract.

axioms (2)

domain assumption Infinite-U Hubbard model in which double occupancy is strictly forbidden.
Standard limit of the Hubbard Hamiltonian invoked to simplify the Hilbert space.
domain assumption Dilute limit with fixed number of doped holes.
Restricts the problem to a sector where the spectrum can be constructed explicitly.

pith-pipeline@v0.9.0 · 5487 in / 1336 out tokens · 45692 ms · 2026-05-13T20:21:25.136703+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

D(T)=β/N(1−I2(2β)/I0(2β)) … upon regularizing … δ(ω)=η/π(η²+ω²) … ρ(T)=η/(2D(T))
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean LogicNat embed_eq_pow unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

energy spectrum E(m)=2 cos(2πm/N)

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

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