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.

Correlation properties of a one-dimensional repulsive Bose gas at finite temperature

“…Asymptotic analytical limits have been described by a variety of physical models [13,14] and compared with the exact solution provided by the thermal Bethe-ansatz (TBA) method within the Yang-Yang theory [15,16]. A new intriguing quantum regime in a 1D Bose gas has been recently predicted by the same authors of the present manuscript [14]. It is signaled by a thermal anomaly in the temperature dependence of the specific heat for any finite value of the interaction strength.…”

“…Distinct quantum regimes can be conveniently classified by the characteristic behavior of thermodynamic properties. Asymptotic analytical limits have been described by a variety of physical models [13,14] and compared with the exact solution provided by the thermal Bethe-ansatz (TBA) method within the Yang-Yang theory [15,16]. A new intriguing quantum regime in a 1D Bose gas has been recently predicted by the same authors of the present manuscript [14].…”

“…The PIMC is a powerful stochastic method which allows to obtain numerically structural and energetic properties of a quantum system at finite temperature [66] which is described here by the microscopic Hamiltonian (1). Some information on the structure of the excitation spectrum can be inferred as well from the dynamic structure factor by using the inverse Laplace transform [14]. PIMC method relies on the Feynman path-integral description of an ensemble of N quantum atoms in terms of a set of N classical polymers, each of them reproducing a quantum delocalized particle [66].…”

“…The excitation of momentum modes with temperature is the origin of highly enhanced density and phase fluctuations which prevent the off-diagonal long-range order [6,7] and then the formation of a true BEC. Instead, an extraordinarily rich landscape of many different degenerate regimes emerges [8][9][10][11][12][13][14], which are separated by smooth crossovers and they might or not share the typical features of a BEC. They can be explored by changing the interaction strength and temperature.…”

“…It is signaled by a thermal anomaly in the temperature dependence of the specific heat for any finite value of the interaction strength. Calculations of the dynamic structure factor with the ab-initio Path Integral Monte Carlo (PIMC) method showed that, at temperatures similar to the anomaly threshold, the excitation pattern experiences the breakdown of the quasiparticle description holding instead at low temperature [14]. Both behaviors of the specific heat and the dynamic structure factor suggest that the novel so-called hole anomaly, which is induced by the presence of unpopulated states in the excitation spectrum of the system, is a reminiscence of the superfluid-normal phase transition at the critical temperature, although any phase transition is not allowed in 1D geometry [17].…”