Quantum anomaly and thermodynamics of one-dimensional fermions with three-body interactions

TL;DR

This paper explores the scale anomaly in a novel one-dimensional fermionic system with three-body interactions, revealing its effects on thermodynamics and connecting it to known two-dimensional anomalies.

Contribution

It introduces the first study of scale anomaly in 1D fermions with three-body contact interactions and analyzes its thermodynamic implications.

Findings

The system exhibits a scale anomaly related to 2D fermions with two-body forces.

The anomaly affects the equation of state and modifies Tan's contact for three-body forces.

The third-order virial coefficient relates to the 2D two-body case.

Abstract

We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body forces. We show, furthermore, that those two cases (and their multi species generalizations) are the only non-relativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well-known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the latter, we calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, we show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case.