A Phase Transition in a Quantum Crystal with Asymmetric Potentials

TL;DR

This paper demonstrates a phase transition in a quantum crystal with asymmetric potentials, showing that polarization becomes discontinuous under certain conditions in high-dimensional systems with strong interactions.

Contribution

It proves the existence of a phase transition in a quantum anharmonic oscillator system with asymmetric potentials, using path measure representations and infrared estimates.

Findings

Discontinuous polarization at a critical external field for d≥3.

Phase transition occurs with large particle mass and interaction strength.

Utilizes path measures and Garsia-Rodemich-Rumsey inequality for proof.

Abstract

A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it might have no symmetry. For this system, we prove that the global polarization (obtained in the thermodynamic limit) gets discontinuous at a certain value of the external field provided $d\geq 3$, and the particle mass as well as the interaction intensity are big enough. The proof is based on the representation of local Gibbs states in terms of path measures and thereby on the use of the infrared estimates and the Garsia-Rodemich-Rumsey inequality.