Ferromagnetic behaviour in the strongly interacting two-component Bose gas

TL;DR

This paper studies the low-temperature thermodynamics of a strongly interacting 1D two-component Bose gas, revealing ferromagnetic effects and unique thermodynamic signatures distinct from spinless Bose gases.

Contribution

It provides an analytical investigation of ferromagnetic behavior in the integrable two-component Bose gas, connecting thermodynamics with effective ferromagnetic models.

Findings

Ferromagnetic states significantly influence low-temperature thermodynamics.

Zero-field susceptibility exceeds that of a free spin paramagnet.

Specific heat and susceptibility exhibit critical exponents indicating ferromagnetism.

Abstract

We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat $c_v \sim T^{1/2}$ and the susceptibility $\chi \sim T^{-2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.