Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model

TL;DR

This paper studies the thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model, combining analytical and numerical methods to explore its properties at finite temperatures and densities.

Contribution

It provides a comprehensive analysis of the thermodynamics and correlation functions of the quantum hard rod model, demonstrating its Tomonaga-Luttinger liquid behavior across various parameters.

Findings

Excellent agreement between analytical and numerical results for thermodynamic quantities.

Hard rod model exhibits Tomonaga-Luttinger liquid behavior over a wide parameter range.

Correlation functions can be used to extract Tomonaga-Luttinger parameters and thermal length.

Abstract

The one-dimensional hard rod model describes impenetrable bosons with finite diameter, extending the Lieb-Liniger model to systems with excluded volume interactions. Here, we investigate the thermodynamics of quantum HRs using Yang-Yang theory, path integral quantum Monte-Carlo calculations, and Luttinger liquid theory. We first discuss the behavior of characteristic thermodynamic quantities, exhibiting deviations to the Lieb-Liniger model for sufficiently high densities, with excellent agreement between analytical and numerical results. We then show that the hard rod model exhibits Tomonaga-Luttinger liquid behavior across a wide range of parameters, at zero and finite temperature, as unveiled by correlation functions. The Tomonaga-Luttinger parameter and thermal length can be extracted by fitting correlation functions to Tomonaga-Luttinger liquid theory, hence demonstrating a robust method for thermometry. This work provides a comprehensive study of strongly correlated hard rod systems at finite temperatures, with applications to quantum wires, spin chains, and ultracold atoms.