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

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 quasiparticle 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.