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Journal of Low Temperature Physics

Effect of Inter-particle Interactions on Pair Correlations of One-Dimensional Anyon Gases

Yan Li, Zhi He

Published Jul 6, 2015• 2 citations
Publisher
DOI
10.1007/s10909-015-1322-x

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A significant feature of the one-dimensional super Tonks-Girardeau gas is its metastable gas-like state with a stronger Fermi-like pressure than for free fermions which prevents a collapse of atoms. This naturally suggests a way to search for such strongly correlated behavior in systems of interacting fermions in one dimension. We thus show that the strongly attractive Fermi gas without polarization can be effectively described by a super Tonks-Girardeau gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A natural description of such super Tonks-Girardeau gases is provided by Haldane generalized exclusion statistics. In particular, they are equivalent to ideal particles obeying more exclusive statistics than Fermi-Dirac statistics.
In February 2026, Hidalgo-Sacoto et al. (OIST/Oklahoma) demonstrated that anyons — particles with exchange statistics intermediate between bosonic and fermionic — can exist in one-dimensional systems, with a continuously tunable exchange factor controlled by interaction strength. This volume proves that this result is a direct consequence of the algebraic framework of Project T. We establish the Anyon Theorem: the commutation deficit C(K) = K(K−3)/2 determines whether a rank-K system admits discrete or continuous exchange statistics. Specifically: (1) C(K) = 0 (uniquely K = 3) forces the exchange factor to be exactly ±1, yielding only bosons and fermions; (2) C(K) > 0 (K ≥ 4) opens escape routes through commuting pairs, allowing the exchange factor to vary continuously — producing anyons; (3) the continuous tunability observed by OIST maps precisely onto the irrational coupling constants of collapsed ranks K ≥ 4. The framework makes a falsifiable prediction: in any system where the effective algebraic rank can be experimentally tuned, the transition from discrete to continuous exchange statistics should occur at the critical point where C(K) first becomes nonzero. The OIST experiment, performed in ultracold atomic gases with tunable interactions, represents the first independent confirmation of the dimensional collapse mechanism predicted by Volume VI. Keywords: anyons, exchange statistics, Yang-Baxter equation, commutation deficit, dimensional collapse, 0-Hecke monoid, ultracold atoms, braiding, Lean 4
The pseudogap is a ubiquitous phenomenon in strongly correlated systems, such as high-T c superconductors, ultracold atoms, and nuclear physics.Whereas pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental one-dimensional models, that is, Gaudin-Yang model.In this paper, we show how the pseudogap effect emerges in the single-particle excitation in this system using a diagrammatic approach.Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to the pseudogap state with increasing the attractive interaction and the number density at finite temperature.Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, indicating the validity of our approach even in the region where the pseudogap appears.