Virial Expansion for a Three-Component Fermi Gas in One Dimension: The Quantum Anomaly Correspondence

TL;DR

This paper investigates the thermodynamics of a three-component Fermi gas in one dimension with a three-body interaction, revealing an exact mapping to two-dimensional two-body anomalous systems in the high temperature limit.

Contribution

It establishes an exact correspondence between three-body interactions in one dimension and two-body interactions in two dimensions under high temperature conditions.

Findings

Identifies the quantum anomaly breaking scale invariance in 1D three-component Fermi gases.

Derives an exact mapping between 1D three-body and 2D two-body anomalous interactions.

Shows thermodynamics are governed by few-body correlations in the high temperature regime.

Abstract

In this paper we explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction is scale invariant in one dimension. However, upon quantization, an anomaly appears which breaks the scale invariance. This is very similar to the physics of two-component fermions in two spatial dimensions, where the two-body interaction is also anomalous. Previous studies have already hinted that the physics of these two systems are intimately related. Here we expand upon those studies by examining the thermodynamic properties of this anomalous one dimensional system in the high temperature limit. We show there is an exact mapping between the traditional two-body anomalous interaction in two dimensions, to that of three-body interaction in one dimension. This result is valid in the high temperature limit, where the thermodynamics can be understood in terms of few-body correlations.