Virial expansion for a three-component Fermi gas in one dimension: The quantum anomaly correspondence

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.

Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime

“…(3) 0 replacing w 0 in Eq. ( 16), has been shown to be important for realistic two-body interactions in one dimension with large scattering length [61], where the three-body interaction and its three-body range correction dominate low-energy physics [61][62][63][64][65][66][67][68].…”

Efimov-like physics in fraction-dimensional Bose systems with three-body interaction

“…It was shown that this system features a scale anomaly, which impacts the thermodynamics [5] and exact universal relations generalizing the Tan contact theorems for three-body forces. The quantum anomaly also affects [6] the high-temperature transport properties of the three-component Fermi gases.…”

Virial coefficients of trapped and untrapped three-component fermions with three-body forces in arbitrary spatial dimensions

“…Motivated by the recent interest in one-dimensional (1D) Fermi and Bose gases in the fine-tuned situation where only three-body interactions are present [1][2][3][4][5][6][7][8][9], we explore here the thermodynamics of fermions with a contact three-body interaction in the region of low fugacity (which corresponds to a dilute regime and therefore high temperatures in units of the energy scale set by the density). We focus on the fermionic case but explore the problem in arbitrary dimension d. To that end, we implement a semiclassical lattice approximation (SCLA) to calculate the virial coefficients b n , and carry out their evaluation up to n = 5 at leading order (LO) in that approximation.…”