Universality class of quantum criticality for strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction

TL;DR

This paper investigates the quantum critical behavior of strongly repulsive spin-1 bosons in one dimension, deriving exact thermodynamic properties and identifying universal critical exponents beyond traditional Tomonaga-Luttinger liquid theory.

Contribution

It provides an analytical derivation of the equation of state and explicit scaling functions, revealing the universality class of quantum criticality in this system.

Findings

Quantum critical points have dynamical exponent z=2 and correlation length exponent ν=1/2.

Quantum criticality can be observed from finite temperature density and magnetization profiles.

Results extend understanding of quantum critical behavior beyond Tomonaga-Luttinger liquid theory.

Abstract

Using the thermodynamic Bethe ansatz equations we study the quantum phase diagram, thermodynamics and criticality of one-dimensional spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions. We analytically derive a high precision equation of state from which the Tomonaga-Luttinger liquid physics and quantum critical behavior of the system are computed. We obtain explicit forms for the scaling functions near the critical points yielding the dynamical exponent $z=2$ and correlation length exponent $\nu=1/2$ for the quantum phase transitions driven by either the chemical potential or the magnetic field. Consequently, we further demonstrate that quantum criticality of the system can be mapped out from the finite temperature density and magnetization profiles of the 1D trapped gas. Our results provide the physical origin of quantum criticality in a 1D many-body system beyond the Tomonaga-Luttinger liquid description.