Rigorous Proof of Pseudospin Ferromagnetism in Two-Component Bosonic Systems with Component-Independent Interactions

TL;DR

This paper rigorously proves that two-component bosonic systems with component-independent interactions have a ferromagnetic ground state with fully polarized pseudospin, and analyzes their spin-wave excitations.

Contribution

It provides a rigorous proof of pseudospin ferromagnetism in two-component bosonic systems with component-independent interactions, including analysis of spin-wave excitations.

Findings

Ground state is a fully polarized pseudospin ferromagnet

Spin-wave excitations exhibit quadratic dispersion at long wavelengths

Applicable to a wide range of real Hamiltonians with component-independent parameters

Abstract

For a two-component bosonic system, the components can be mapped onto a pseudo-spin degree of freedom with spin quantum number S=1/2. We provide a rigorous proof that for a wide-range of real Hamiltonians with component independent mass and interaction, the ground state is a ferromagnetic state with pseudospin fully polarized. The spin-wave excitations are studied and found to have quadratic dispersion relations at long wave length.