We study the thermal behavior of correlations in a one-dimensional Bose gas with tunable interaction strength, crossing from weakly repulsive to the Tonks-Girardeau regime. A reference temperature in this system is that of the hole anomaly, observed as a peak in the specific heat and a maximum in the chemical potential. 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 $1/{\left|k\right|}^3$ 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 ${\left|x\right|}^3$ dependence disappears for temperatures above the anomaly. We obtain a 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 calculations for the momentum distribution and the OBDM exploring a wide range of interaction strength and temperature. Our results unveil a 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.

Close

PrevNext

View figure in article

• Bosons
• Cold atoms & matter waves
• Hard-core bosons
• Nuclear many-body theory
• Quasiparticles & collective excitations
• Spinless fermions
• Temperature
• Thermal properties
• Thermodynamics
• 1-dimensional systems
• Bose gases
• Quantum many-body systems
• Ultracold gases
• Bethe ansatz
• Correlation function measurements
• Path-integral Monte Carlo