Anomalous energy transport in the Berezinskii-Kosterlitz-Thouless phase

TL;DR

This paper investigates energy transport in the XY model, revealing that in the Berezinskii-Kosterlitz-Thouless phase, energy diffusivity diverges logarithmically due to spin-wave excitations, contrasting with normal diffusion in other phases.

Contribution

It provides a theoretical analysis of anomalous energy transport in the BKT phase using nonlinear fluctuating hydrodynamics and renormalization group methods.

Findings

Fourier's law holds in most phases and dimensions.

Energy diffusivity diverges logarithmically in the BKT phase.

Elastic energy transport is driven by spin-wave excitations.

Abstract

We study nonlinear fluctuating hydrodynamic theories with charge and energy conservation in and above two dimensions that describe the large-scale behavior of the Hamiltonian XY model in the disordered and ordered phases. Using renormalization group analysis at one-loop order, we show that while Fourier's law holds in the ordered phase above two dimensions and in the disordered phase in any dimension, the energy diffusivity in the ordered phase exactly in two dimensions, the Berezinskii-Kosterlitz-Thouless phase, exhibits a logarithmic divergence in the thermodynamic limit. This divergence arises from elastic energy transport induced by spin-wave excitations.