Universality and quantum criticality of the one-dimensional spinor Bose gas

TL;DR

This paper explores the universal thermodynamics and quantum critical behavior of a two-component one-dimensional Bose gas, revealing unique critical properties, phase transitions, and experimental signatures relevant for ultracold atomic gases.

Contribution

It identifies the universality class of the quantum critical point and characterizes the momentum distribution and thermodynamic ratios near criticality, highlighting novel quantum phenomena.

Findings

Quantum critical region belongs to a distinct universality class from the single-component case.

The compressibility Wilson ratio effectively distinguishes quantum regimes.

Universal contact exhibits a minimum in the Tonks-Girardeau regime, indicating phase transition.

Abstract

We investigate the universal thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. We find that the quantum critical region belongs to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case and identify its boundaries with the peaks of the specific heat. In addition, we show that the compressibility Wilson ratio, which quantifies the relative strength of thermal and quantum fluctuations, serves as a good discriminator of the quantum regimes near the quantum critical point. Remarkably, in the Tonks-Girardeau regime the universal contact develops a pronounced minimum, reflected in a counterintuitive narrowing of the momentum distribution as we increase the temperature. This momentum reconstruction, also present at low and intermediate momenta, signals the transition from the ferromagnetic to the spin-incoherent Luttinger liquid phase and can be detected in current experiments with ultracold atomic gases in optical lattices.