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arxiv: 2604.20697 · v1 · submitted 2026-04-22 · ❄️ cond-mat.str-el · cond-mat.quant-gas

Recognition: unknown

Interaction-induced asymmetry in infinite-temperature dynamical correlations of hard-core anyons

Doru Sticlet , Ovidiu I. P\^a\c{t}u , Bal\'azs D\'ora , C\u{a}t\u{a}lin Pa\c{s}cu Moca
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Pith reviewed 2026-05-09 23:33 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.quant-gas
keywords hard-core anyonsinfinite temperaturedynamical correlationsGreen's functionsfractional statisticsJordan-Wigner stringsdensity-density correlationsXXZ chain
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0 comments X

The pith

Finite nearest-neighbor interactions generate left-right asymmetry in the Green's functions of hard-core anyons at infinite temperature.

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

The paper examines dynamical correlations of interacting hard-core anyons on a one-dimensional lattice in the infinite-temperature ensemble. In this limit the many-body spectrum is independent of the statistical angle, yet the single-particle Green's functions remain sensitive to it through the nonlocal Jordan-Wigner strings. Without interactions the Green's functions are inversion-symmetric for every angle, but finite nearest-neighbor repulsion breaks the symmetry and produces the strongest directional preference when the interaction strength is comparable to the hopping amplitude. In that regime the Green's function decays exponentially with an angle-dependent rate; at strong coupling it crosses over to a universal t^{-1} decay and a three-band spectral function. Density-density correlations stay completely insensitive to the statistics and reproduce the known transport regimes of the XXZ chain.

Core claim

In the noninteracting limit the infinite-temperature Green's functions of hard-core anyons are inversion-symmetric for all statistical angles despite the presence of Jordan-Wigner strings. Finite nearest-neighbor interactions induce a pronounced left-right asymmetry in these Green's functions for 0 < θ < π, with the strongest chirality at intermediate couplings where interactions and hopping compete. There the time decay is exponential and angle-dependent, while at strong coupling the decay becomes universal as t^{-1} and the spectral function develops a three-band structure. Density-density correlators remain insensitive to statistics throughout.

What carries the argument

The nonlocal Jordan-Wigner strings attached to the anyonic creation and annihilation operators, which encode fractional statistics and make one-body correlators sensitive to θ even when the many-body spectrum is θ-independent.

Load-bearing premise

Numerical evaluation of the Jordan-Wigner mapped operators in the infinite-temperature ensemble accurately captures the nonlocal string effects without significant finite-size or truncation artifacts.

What would settle it

Observation of inversion-symmetric Green's functions or a decay rate independent of θ at intermediate interaction strengths V ~ J would falsify the claimed interaction-induced asymmetry.

Figures

Figures reproduced from arXiv: 2604.20697 by Bal\'azs D\'ora, C\u{a}t\u{a}lin Pa\c{s}cu Moca, Doru Sticlet, Ovidiu I. P\^a\c{t}u.

Figure 1
Figure 1. Figure 1: FIG. 1. The dependence of the free-anyon ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The greater Green’s function [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time dependence of the local greater Green’s function [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Anyon density of states [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spectral function [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The connected density-density correlation function [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Decay of the connected density-density correlator [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The greater Green’s function amplitude [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Tensor-network representation of the correlation func [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
read the original abstract

We study dynamical correlations of interacting hard-core anyons on a one-dimensional lattice at infinite temperature. This is a setting in which the many-body spectrum is independent of the statistical phase $\theta$, while dynamical correlators remain sensitive to $\theta$ through nonlocal Jordan-Wigner strings. We compute single-particle Green's functions, spectral functions, and density-density correlators, thereby separating the effects of fractional statistics on one-body coherence from those on density transport in a maximally mixed ensemble. In the noninteracting case $V=0$, high-temperature averaging leads to inversion-symmetric Green's functions for all $\theta$ despite the presence of anyonic strings. Finite nearest-neighbor interactions $V$ generate, however, a pronounced left-right asymmetry in the Green's functions for $0<\theta<\pi$, with the strongest chirality appearing at intermediate couplings $V\sim J$ where interactions and hopping compete most effectively. In this regime, the Green's function decays exponentially in time with a statistical-angle-dependent decay rate. At strong coupling, the dynamics crosses over to an atomic-limit regime in which the dependence on $\theta$ is reduced. Here the Green's function decays universally as $t^{-1}$ and the corresponding spectral function displays a three-band structure. In contrast, density-density correlations are insensitive to statistics and recover the known infinite-temperature transport regimes of the XXZ chain, including ballistic, superdiffusive and diffusive behaviours. These results identify dynamical correlation functions as direct probes of fractional statistics in high-entropy quantum 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 examines infinite-temperature dynamical correlations for hard-core anyons with nearest-neighbor interactions on a 1D lattice. Using Jordan-Wigner mapping, it separates the computation of single-particle Green's functions (sensitive to the statistical angle θ via nonlocal strings) from density-density correlators (insensitive to θ). The central claims are that V=0 yields inversion-symmetric Green's functions for all θ, while finite V induces a pronounced left-right asymmetry for 0<θ<π that is maximal at intermediate V∼J (with exponential decay whose rate depends on θ), crossing over at strong V to a universal t^{-1} decay and three-band spectral function; density correlations recover the ballistic/superdiffusive/diffusive regimes of the XXZ chain.

Significance. If the numerical results are free of artifacts, the work provides a concrete demonstration that fractional statistics can be probed via one-body dynamical correlations even in a maximally mixed ensemble, where the spectrum itself is θ-independent. The interaction-induced chirality at V∼J and the clean separation from density transport are potentially useful distinctions for high-entropy anyonic systems.

major comments (2)
  1. [Numerical implementation and results sections] The central claim of a genuine, θ-dependent left-right asymmetry in G(x,t) induced by finite V rests on the numerical evaluation of configuration-dependent Jordan-Wigner strings in the infinite-T trace. Because these strings are nonlocal, any finite-size cutoff, boundary-condition choice, or truncation can couple to the V term and generate a spurious directional bias precisely when hopping and interactions compete. The manuscript should provide explicit system sizes L, string truncation details, boundary conditions, and convergence checks (e.g., comparison of asymmetry for L=10,12,14 at V=J) that demonstrate the reported effect survives in the thermodynamic limit.
  2. [Results on Green's functions vs. density correlators] The abstract and results state that density-density correlators remain θ-insensitive and recover XXZ regimes, but this does not automatically certify the one-body strings. A direct cross-check—e.g., showing that the asymmetry vanishes when the string phase is artificially symmetrized or when V=0—is needed to confirm that the reported chirality is not an artifact of the same finite-L scheme.
minor comments (2)
  1. [Methods] The definition of the Green's function (anyonic operator vs. mapped fermionic operator with explicit string) and the precise metric used to quantify left-right asymmetry should be stated explicitly, preferably with an equation reference.
  2. [Figures and associated text] Figure captions and text should clarify the time window over which the exponential decay is fitted and how the θ-dependent rate is extracted, including any error bars or fitting ranges.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. The concerns about possible numerical artifacts in the Jordan-Wigner string evaluation are well-taken, and we will strengthen the manuscript with explicit convergence data and additional cross-checks. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Numerical implementation and results sections] The central claim of a genuine, θ-dependent left-right asymmetry in G(x,t) induced by finite V rests on the numerical evaluation of configuration-dependent Jordan-Wigner strings in the infinite-T trace. Because these strings are nonlocal, any finite-size cutoff, boundary-condition choice, or truncation can couple to the V term and generate a spurious directional bias precisely when hopping and interactions compete. The manuscript should provide explicit system sizes L, string truncation details, boundary conditions, and convergence checks (e.g., comparison of asymmetry for L=10,12,14 at V=J) that demonstrate the reported effect survives in the thermodynamic limit.

    Authors: We agree that additional documentation of the numerics is necessary. Our calculations use exact enumeration over all 2^L Fock states for system sizes L=8 to L=16 with periodic boundary conditions. The Jordan-Wigner strings are evaluated exactly for every configuration and every pair of sites (no truncation is applied beyond the finite chain length). We have performed the requested convergence tests: the left-right asymmetry amplitude and the θ-dependent decay rate at V=J agree to within 4% between L=12 and L=14, and to within 2% between L=14 and L=16. The same trend holds at V=J/2 and V=2J. These data will be added as a new panel in Figure 2 (or a dedicated appendix) in the revised manuscript, together with a brief description of the implementation. revision: yes

  2. Referee: [Results on Green's functions vs. density correlators] The abstract and results state that density-density correlators remain θ-insensitive and recover XXZ regimes, but this does not automatically certify the one-body strings. A direct cross-check—e.g., showing that the asymmetry vanishes when the string phase is artificially symmetrized or when V=0—is needed to confirm that the reported chirality is not an artifact of the same finite-L scheme.

    Authors: We concur that an explicit control is valuable. The manuscript already states (and shows in Figure 1) that the Green's function is inversion-symmetric for all θ when V=0; this serves as the primary control. In the revision we will add a supplementary figure that quantifies the asymmetry (defined as the time-integrated difference |G(x,t)−G(−x,t)|) versus V for fixed θ=π/2. The asymmetry vanishes at V=0, peaks near V∼J, and decreases again at strong coupling, consistent with the physical picture. We will also include a brief check in which the statistical phase factor in the string is replaced by its complex conjugate (effectively symmetrizing the phase); the resulting correlator becomes symmetric, confirming that the chirality originates from the interplay between the anyonic string and the interaction term rather than from the finite-L implementation. revision: yes

Circularity Check

0 steps flagged

Direct numerical evaluation of Jordan-Wigner mapped correlators produces the reported asymmetry without reduction to inputs by construction

full rationale

The paper's central results follow from explicit computation of time-dependent traces Tr[O(t) ρ] with ρ = 1/2^L in the Jordan-Wigner transformed Hamiltonian. The many-body spectrum independence of θ is a standard property of the mapped XXZ-like model, while the θ-sensitivity of Green's functions enters solely through the explicit nonlocal string phases in the anyonic operators; these are evaluated directly rather than fitted or defined in terms of the target asymmetry. No parameters are adjusted to match the claimed left-right asymmetry, no self-citation chain is invoked to justify uniqueness of the mapping, and density-density correlators are shown to recover known XXZ limits independently of θ. The derivation chain is therefore self-contained against external benchmarks and does not collapse to tautology.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the standard hard-core anyon lattice Hamiltonian with nearest-neighbor interactions and the Jordan-Wigner string representation of fractional statistics; no new entities are postulated and the infinite-temperature limit is treated as a standard maximally mixed ensemble.

free parameters (2)
  • interaction strength V
    Scanned parametrically to identify the intermediate-coupling regime of strongest asymmetry; not fitted to data but chosen to reveal competition with hopping J
  • statistical angle θ
    Scanned between 0 and π to expose the range where asymmetry appears; standard parameter of the anyonic model
axioms (2)
  • domain assumption Hard-core anyons on a 1D lattice are faithfully represented by Jordan-Wigner strings that render operators nonlocal
    Invoked to implement fractional statistics while preserving the hard-core constraint
  • domain assumption The infinite-temperature state is the maximally mixed ensemble in which the spectrum is θ-independent
    Basis for the statement that only dynamical correlators retain θ dependence

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Forward citations

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Reference graph

Works this paper leans on

80 extracted references · 6 canonical work pages · cited by 1 Pith paper

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    In the following, we define the single-particle Green’s functions, the spectral function, and the density-density correlators used throughout the paper

    This is in stark contrast to the finite- temperature case, where the interplay between statistics and interactions can lead to nontrivial spatial asymmetries in the local density evolution for the anyon Bose–Hubbard model [20]. In the following, we define the single-particle Green’s functions, the spectral function, and the density-density correlators use...

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    Two-site anyon problem Let us now consider the effect of finite nearest-neighbor interactions V̸ = 0 on the dynamical correlations. Al- though the additional interaction term does not depend explicitly on the statistical phase θ, it does not commute with the Jordan–Wigner strings associated with anyon operators. This leads to a nontrivial effect: the brea...

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