Quantum criticality of spin-1 bosons in a 1D harmonic trap

TL;DR

This paper explores the universal thermodynamics and quantum critical behavior of spin-1 bosons in a 1D trap, revealing phase structures and critical exponents that resemble those of spin-1/2 Fermi gases.

Contribution

It provides a detailed analysis of quantum criticality and phase diagram for spin-1 bosons, highlighting universal scaling laws and critical exponents.

Findings

Identification of phase structures with partially-polarized cores and spin-singlet or fully spin-aligned wings.

Determination of quantum critical exponents: z=2 and ν=1/2.

Universal scaling behavior of density profiles near quantum critical points.

Abstract

We investigate universal thermodynamics and quantum criticality of spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions in a one-dimensional harmonic trap. From the equation of state, we find that a partially-polarized core is surrounded by two wings composed of either spin-singlet pairs or a fully spin-aligned Tonks-Girardeau gas depending on the polarization. We describe how the scaling behaviour of density profiles can reveal the universal nature of quantum criticality and map out the quantum phase diagram. We further show that at quantum criticality the dynamical critical exponent $z = 2$ and correlation length exponent $\nu=1/2$. This reveals a subtle resemblance to the physics of the spin-1/2 attractive Fermi gas.