Phase diagrams for quantum Brownian motion models on two-dimensional Bravais lattices

TL;DR

This paper analyzes quantum Brownian motion models on various two-dimensional Bravais lattices, deriving phase diagrams and localization behaviors through renormalization group analysis, extending previous one-dimensional studies.

Contribution

It extends quantum Brownian motion analysis from one-dimensional to two-dimensional Bravais lattices, providing detailed phase diagrams and localization insights for different lattice types.

Findings

Localization depends on lattice anisotropy.

Phase boundaries vary with lattice geometry.

Zero temperature flow diagrams are derived.

Abstract

We study quantum Brownian motion (QBM) models for a particle in a dissipative environment coupled to a periodic potential. We review QBM for a particle in a one-dimensional periodic potential and extend the study to that for a particle in two-dimensional (2D) periodic potentials of four Bravais lattice types: square, rectangular, triangular (hexagonal), and centered rectangular. We perform perturbative renormalization group analyses to derive the zero temperature flow diagrams and phase boundaries for a particle in these potentials, and observe localization behavior dependent on the anisotropy of the lattice parameters.