Speaker
Description
We study the thermal behavior of correlations in a one-dimensional Bose gas with tunable interaction strength, crossing from weakly-repulsive to Tonks-Girardeau regime [1-2]. A reference temperature in this system is that of the hole anomaly [3], observed as a peak in the specific heat and a maximum in the chemical potential. At the anomaly temperature, the spectral states located below the hole branch are thermally occupied and the breakdown of the quasi-particle description occurs. We find that at large momenta $k$ and temperature above the anomaly threshold, the tail $\mathcal{C}/k^4$ of the momentum distribution (proportional to the Tan contact $\mathcal{C}$) is screened by the $1/|k|^3$-term due to a dramatic thermal increase of the internal energy emerging from the thermal occupation of spectral excitation states. The same fading is consistently revealed in the behavior at short distances $x$ of the one-body density matrix (OBDM) where the $|x|^3$-dependence disappears for temperatures above the anomaly. We obtain a new general analytic tail for the momentum distribution and a minimum $k$ fixing its validity range, both calculated with exact Bethe-Ansatz method and valid in all interaction and thermal regimes, crossing from the quantum to the classical gas limit. Our predictions are confirmed by comparison with ab-initio Path Integral Monte Carlo (PIMC) calculations for the momentum distribution and the OBDM exploring a wide range of interaction strength and temperature. Our results unveil a novel connection between excitations and correlations. We expect them to be of interest to any cold atomic, nuclear, solid-state, electronic and spin system exhibiting an anomaly or a thermal second-order phase transition.
[1] G. De Rosi, R. Rota, G. E. Astrakharchik, and J. Boronat, Correlation properties of a one-dimensional repulsive Bose gas at finite temperature, New J. Phys. 25 043002 (2023)
[2] G. De Rosi, G. E. Astrakharchik, M. Olshanii, and J. Boronat, Thermal fading of the $1/k^4$-tail of the momentum distribution induced by the hole anomaly, Phys. Rev. A 109, L031302 (2024)
[3] G. De Rosi, R. Rota, G. E. Astrakharchik, and J. Boronat, Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas, SciPost Phys. 13, 035 (2022)
