Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas

TL;DR

This paper uncovers a unique anomaly in the specific heat of a one-dimensional Bose gas, linked to a hole excitation gap, using exact Bethe Ansatz calculations and Monte Carlo simulations, with implications for thermometry and understanding quantum phases.

Contribution

It introduces the first computation of the dynamic structure factor for this system and reveals a temperature-dependent anomaly analogous to phase transitions in higher dimensions.

Findings

Identification of a specific heat peak related to hole excitations.

Exact Bethe Ansatz calculation of the specific heat.

First computation of the dynamic structure factor at finite temperature.

Abstract

We reveal an intriguing anomaly in the temperature dependence of the specific heat of a one-dimensional Bose gas. The observed peak holds for arbitrary interaction and remembers a superfluid-to-normal phase transition in higher dimensions, but phase transitions are not allowed in one dimension. The presence of the anomaly signals a region of unpopulated states which behaves as an energy gap and is located below the hole branch in the excitation spectrum. The anomaly temperature is found to be of the same order of the energy of the maximum of the hole branch. We rely on the Bethe Ansatz to obtain the specific heat exactly and provide interpretations of the analytically tractable limits. The dynamic structure factor is computed with the Path Integral Monte Carlo method for the first time. We notice that at temperatures similar to the anomaly threshold, the energy of the thermal fluctuations become comparable with the maximal hole energy, leading to a qualitative change in the structure of excitations. This excitation pattern experiences the breakdown of the quasi-particle description for any value of the interaction strength at the anomaly, similarly to any superfluid phase transition at the critical temperature. We provide indications for future observations and how the hole anomaly can be employed for in-situ thermometry, identifying different collisional regimes and understanding other anomalies in atomic, solid-state, electronic, spin-chain and ladder systems.