Proof of Bose condensation for weakly interacting lattice bosons

TL;DR

This paper proves the existence of Bose condensation in a weakly interacting lattice Bose gas at low temperatures, using infrared bounds without reflection positivity or expansion methods.

Contribution

It establishes Bose condensation for weakly interacting lattice bosons under small interaction and chemical potential, employing a novel infrared bound approach.

Findings

Bose condensation occurs at low temperature for small interaction.

The method avoids reflection positivity and expansion techniques.

The proof applies to simple cubic lattice Bose gases.

Abstract

A weakly interacting Bose gas on a simple cubic lattice is considered. We prove the existence of the standard or zero-mode Bose condensation at sufficiently low temperature. This result is valid for sufficiently small interaction potential and small values of chemical potential. Our method exploits infrared bound for the suitable two-point Bogolyubov's inner product. We do not use the reflection positivity or some expansion methods.