Sine-Gordon model coupled with a free scalar field emergent in the low-energy phase dynamics of a mixture of pseudospin-1/2 Bose gases with interspecies spin exchange

TL;DR

This paper uses effective field theory to analyze the phase diagram of a pseudospin-1/2 Bose gas mixture, revealing regimes where low-energy excitations are described by a sine-Gordon model coupled with a free scalar field, with implications for experimental probes.

Contribution

It introduces a low-energy effective field theory framework for the mixture, identifying regimes with sine-Gordon coupled fields and deriving RG equations for (1+1)D systems, advancing understanding of phase transitions in such gases.

Findings

Four mean-field regimes identified based on interaction parameters.

In two regimes, low-energy excitations resemble two-component spinless bosons.

In other regimes, excitations are described by a sine-Gordon model coupled with a free scalar field.

Abstract

Using the approach of low-energy effective field theory, the phase diagram is studied for a mixture of two species of pseudospin-$\1/2$ Bose atoms with interspecies spin-exchange. There are four mean-field regimes on the parameter plane of $g_e$ and $g_z$, where $g_e$ is the interspecies spin-exchange interaction strength, while $g_z$ is the difference between the interaction strength of interspecies scattering without spin-exchange of equal spins and that of unequal spins. Two regimes, with $|g_z| > |g_e|$, correspond to ground states with the total spins of the two species parallel or antiparallel along $z$ direction, and the low energy excitations are equivalent to those of two-component spinless Bosons. The other two regimes, with $|g_e| > |g_z|$, correspond to ground states with the total spins of the two species parallel or antiparallel on $xy$ plane, and the low energy excitations are described by a sine-Gordon model coupled with a free scalar field, where the effective fields are combinations of the phases of the original four Boson fields. In (1+1)-dimension, they are described by Kosterlitz-Thouless renormalization group (RG) equations, and there are three sectors in the phase plane of a scaling dimension and a dimensionless parameter proportional to the strength of the cosine interaction, both depending on the densities. The gaps of these elementary excitations are experimental probes of the underlying many-body ground states.