Critical phenomena in one dimension from a Bethe ansatz perspective

TL;DR

This paper reviews recent advances in understanding quantum critical phenomena in one-dimensional integrable quantum gases using Bethe ansatz solutions, highlighting their role in explaining universal behaviors and testable predictions in ultracold atom systems.

Contribution

It provides a comprehensive overview of how Bethe ansatz solutions elucidate quantum criticality and related phenomena in 1D integrable models, connecting theory with experiments.

Findings

Bethe ansatz solutions precisely describe quantum criticality in 1D gases.

Universal thermodynamics and scaling functions are characterized for prototypical models.

Experimental implications for ultracold atomic systems are discussed.

Abstract

This article briefly reviews recent theoretical developments in quantum critical phenomena in one-dimensional (1D) integrable quantum gases of cold atoms. We present a discussion on quantum phase transitions, universal thermodynamics, scaling functions and correlations for a few prototypical exactly solved models, such as the Lieb-Liniger Bose gas, the spin-1 Bose gas with antiferromagnetic spin-spin interaction, the two-component interacting Fermi gas as well as spin-3/2 Fermi gases. We demonstrate that their corresponding Bethe ansatz solutions provide a precise way to understand quantum many-body physics, such as quantum criticality, Luttinger liquids, the Wilson ratio, Tan's Contact, etc. These theoretical developments give rise to a physical perspective using integrability for uncovering experimentally testable phenomena in systems of interacting bosonic and fermonic ultracold atoms confined to 1D.