Charge carriers with fractional exclusion statistics in cuprates

F. Ye; L. Yu; P. A. Marchetti; Z. B. Su

arxiv: 1907.05081 · v1 · pith:VA2ZL3LNnew · submitted 2019-07-11 · ❄️ cond-mat.str-el · hep-th

Charge carriers with fractional exclusion statistics in cuprates

P. A. Marchetti , F. Ye , Z. B. Su , L. Yu This is my paper

Pith reviewed 2026-05-24 23:13 UTC · model grok-4.3

classification ❄️ cond-mat.str-el hep-th

keywords exclusion statisticst-J modelcupratesFermi volumeno-double-occupationspin-charge gaugefractional statisticshole-doped superconductors

0 comments

The pith

Spinless charge carriers in the 2D t-J model obey exclusion statistics with parameter 1/2 from the no-double-occupation constraint.

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

The paper establishes that in the SU(2) x U(1) spin-charge gauge approach, the spinless charge carriers in the two-dimensional t-J model can be consistently assigned an exclusion statistics parameter of 1/2. This fractional statistics arises from the no-double-occupation constraint, mirroring the one-dimensional case. Applying this statistics recovers a large Fermi volume for holes at high doping levels, similar to the tight-binding approximation. The weakly bound composite structure of the hole then accounts for several anomalous properties observed in hole-doped cuprate superconductors.

Core claim

In the SU(2)XU(1) spin-charge gauge approach applied to the t-J model, the spinless charge carriers in 2D exhibit exclusion statistics with g=1/2, originating from the no-double-occupation constraint, just as in 1D. This allows recovery of a large Fermi volume of holes at high dopings, close to the tight-binding result, and provides an explanation for experimental features via the composite hole nature.

What carries the argument

The SU(2) x U(1) spin-charge gauge approach that permits assigning exclusion statistics g=1/2 to spinless charge carriers based on the no-double-occupation constraint.

If this is right

A large Fermi volume of holes is recovered at high dopings, close to the tight-binding approximation.
The composite nature of the hole, made of weakly bound charge and spin carriers, explains many unusual experimental features of hole-doped cuprates.
The fractional exclusion statistics with parameter 1/2 holds in 2D as it does in 1D due to the no-double-occupation constraint.

Where Pith is reading between the lines

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

Signatures of g=1/2 statistics could appear in specific heat or magnetic susceptibility measurements at varying doping levels.
The approach may connect to explanations of the pseudogap or pairing in cuprates through the composite carrier structure.
Similar statistics assignments might apply to other lattice models with strict occupancy constraints.

Load-bearing premise

The SU(2)XU(1) spin-charge gauge approach is applicable to the 2D t-J model and supports a consistent assignment of exclusion statistics g=1/2 based on the no-double-occupation constraint.

What would settle it

A measurement showing that the Fermi surface volume at high doping deviates significantly from the large volume predicted or that thermodynamic data yield an effective exclusion parameter different from 1/2.

read the original abstract

We show that in the SU(2)XU(1) spin-charge gauge approach we developed earlier one can attribute consistently an exclusion statistics with parameter 1/2 to the spinless charge carriers of the t-J model in two dimensions(2D), as it occurs in one dimension (1D). Like the 1D case, the no-double occupation constraint is at the origin of this fractional exclusion statistics. With this statistics we recover a "large" Fermi volume of holes at high dopings, close to that of the tight binding approximation. Furthermore, the composite nature of the hole, made of charge and spin carriers only weakly bounded, can provide a natural explanation of many unusual experimental features of the hole-doped cuprates.

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

This extends the authors' gauge theory to assign g=1/2 exclusion statistics to 2D t-J holes and recover large FS volume, but the step from 1D relies entirely on their prior framework.

read the letter

The key takeaway is that this work extends the authors' SU(2)xU(1) gauge theory to assign g=1/2 Haldane exclusion statistics to the spinless holes in the 2D t-J model, based on the no-double-occupancy constraint, and uses that to recover a large Fermi surface volume matching the tight-binding result at high doping. What stands out is how they link this statistics directly to the composite hole picture, where charge and spin are weakly bound. This organizes the large FS issue under one framework, which is a longstanding problem in cuprate physics. The 1D case is known, so the 2D consistency is the step forward here. The main limitation is that everything hinges on their earlier gauge approach being valid in 2D without introducing inconsistencies in the quasiparticle counting. The abstract states it as consistent, but without seeing explicit derivations or comparisons to other methods like DMFT or numerics, it's hard to judge how robust the g=1/2 assignment is when gauge fields are integrated out. The circularity with their own prior papers is real, though self-citation for a framework is expected. This paper is for specialists in gauge theories of high-Tc or fractional statistics in condensed matter. A reader already familiar with the Marchetti-Yu line of work will get the most out of it, as it builds directly on that. It deserves a serious referee because the claim is concrete enough to be tested against the 1D analog or against ARPES data on FS volume, even if the evidence in this manuscript is mostly within their model. I would recommend sending it to peer review rather than desk rejecting it.

Referee Report

2 major / 0 minor

Summary. The paper claims that within the authors' SU(2)×U(1) spin-charge gauge theory applied to the 2D t-J model, the spinless charge carriers obey Haldane exclusion statistics with parameter g=1/2 originating from the no-double-occupation constraint (as in 1D), and that this assignment recovers a large Fermi volume of holes at high doping close to the tight-binding result while the composite hole nature explains cuprate anomalies.

Significance. If the consistent assignment of g=1/2 holds independently, the result would link fractional exclusion statistics directly to the projector constraint and provide a mechanism for Fermi-surface evolution in cuprates. The manuscript does not supply new machine-checked derivations, reproducible code, or falsifiable predictions beyond the framework-internal consistency already claimed in prior works.

major comments (2)

[Abstract] Abstract: the central claim that g=1/2 can be 'attributed consistently' to the charge carriers in 2D rests on the applicability of the SU(2)×U(1) gauge approach, yet the text provides no explicit derivation showing how the local no-double-occupation projector maps onto the specific Haldane parameter g=1/2 in the 2D gauge-fixed theory without additional dynamical assumptions on the gauge fields.
[Abstract] Abstract: the recovery of a 'large' Fermi volume at high dopings is asserted to be close to the tight-binding result, but no quantitative comparison, doping dependence, or explicit quasiparticle counting formula is given to substantiate that the g=1/2 statistics produces this volume without further tuning.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond to each major comment in turn.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that g=1/2 can be 'attributed consistently' to the charge carriers in 2D rests on the applicability of the SU(2)×U(1) gauge approach, yet the text provides no explicit derivation showing how the local no-double-occupation projector maps onto the specific Haldane parameter g=1/2 in the 2D gauge-fixed theory without additional dynamical assumptions on the gauge fields.

Authors: The SU(2)×U(1) gauge approach to the t-J model, as introduced in our earlier works, incorporates the no-double-occupation constraint through the gauge fields in a way that naturally leads to the Haldane exclusion statistics parameter g=1/2 for the spinless charge carriers. This is shown to be consistent in both 1D and 2D within the framework. The current manuscript assumes familiarity with that derivation and focuses on its application to the Fermi volume. However, to make the manuscript more self-contained, we will include a concise summary of the key mapping in a revised version. revision: partial
Referee: [Abstract] Abstract: the recovery of a 'large' Fermi volume at high dopings is asserted to be close to the tight-binding result, but no quantitative comparison, doping dependence, or explicit quasiparticle counting formula is given to substantiate that the g=1/2 statistics produces this volume without further tuning.

Authors: The explicit quasiparticle counting formula for exclusion statistics is standard in the literature on Haldane statistics and is applied here with g=1/2. At high doping, this yields a Fermi volume approaching that of the tight-binding model for holes because the fractional statistics effectively incorporates the spin-charge separation. We acknowledge that a direct quantitative comparison would strengthen the claim and will add such a comparison, including the doping dependence, in the revised manuscript. revision: yes

Circularity Check

1 steps flagged

Attribution of g=1/2 exclusion statistics in 2D t-J model rests on authors' prior SU(2)×U(1) gauge approach

specific steps

self citation load bearing [Abstract]
"We show that in the SU(2)XU(1) spin-charge gauge approach we developed earlier one can attribute consistently an exclusion statistics with parameter 1/2 to the spinless charge carriers of the t-J model in two dimensions(2D), as it occurs in one dimension (1D). Like the 1D case, the no-double occupation constraint is at the origin of this fractional exclusion statistics."

The consistent attribution of the specific value g=1/2 (and the resulting large Fermi volume) is presented as possible only inside the gauge approach developed earlier by the same authors. The paper does not derive the mapping from the local no-double-occupation projector to g=1/2 independently in 2D; it relies on the prior framework to make the assignment 'consistent,' rendering the central result load-bearing on self-citation.

full rationale

The paper's core claim—that one can consistently assign Haldane exclusion parameter g=1/2 to spinless charge carriers in 2D, originating from the no-double-occupation constraint and recovering a large Fermi volume—is explicitly conditioned on the applicability of the SU(2)×U(1) spin-charge gauge framework developed in the authors' earlier papers. The abstract and introduction frame the 2D result as an extension 'as it occurs in 1D' within that pre-existing approach, without providing an independent derivation or external benchmark for the specific g value in 2D. This matches self-citation load-bearing: the load-bearing step (consistent attribution and quasiparticle counting) reduces to the prior self-cited framework rather than a self-contained derivation from the t-J model alone.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the prior development of the SU(2)XU(1) gauge theory and the assumption that no-double-occupancy directly implies g=1/2 statistics in 2D as in 1D; no free parameters or new entities are explicitly introduced in the abstract.

axioms (2)

domain assumption The SU(2)XU(1) spin-charge gauge approach is valid for the 2D t-J model.
Invoked as the framework in which the statistics attribution is shown to be consistent.
domain assumption No-double-occupation constraint implies exclusion statistics parameter 1/2 in 2D.
Stated as the origin of the fractional statistics, analogous to 1D.

pith-pipeline@v0.9.0 · 5657 in / 1518 out tokens · 21638 ms · 2026-05-24T23:13:11.898727+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.

one can attribute consistently an exclusion statistics with parameter 1/2 to the spinless charge carriers ... the no-double occupation constraint is at the origin of this fractional exclusion statistics
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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

if 2πσ_H = 1 we have g = α ... Hall conductivity 1/(2π) ... semionic holons ... exclusion statistics parameter 1/2

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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.
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