"Polar" and "antiferromagnetic" order in f=1 many-boson systems

TL;DR

This paper proves inequalities indicating polar or antiferromagnetic order in f=1 boson systems, revealing a phase transition at zero quadratic Zeeman energy and highlighting the conditions for different magnetic orders.

Contribution

It introduces new inequalities for the ground state density of spin-0 bosons, demonstrating phase transitions and magnetic order in f=1 boson systems.

Findings

Ground state exhibits polar or antiferromagnetic order for large q

Sharp transition at q=0 in low density limit

Inequalities establish conditions for magnetic ordering

Abstract

In a system of interacting f=1 bosons (in the subspace where the total spin in the z-direction is vanishing), we prove inequalities for the ground state expectation value of the density of spin-0 bosons. The inequalities imply that the ground state possesses "polar" or "antiferromagnetic" order when the quadratic Zeeman term q is large enough. In the low density limit, the inequalities establish the existence of a sharp transition at q=0 when q is varied.