Diffusion and signatures of localization in stochastic conformal field theory

TL;DR

This paper introduces a stochastic conformal field theory model to study the effects of random impurities, revealing localization, vanishing energy currents, and a crossover from ballistic to diffusive energy transport.

Contribution

It presents a novel model of stochastic conformal field theory that captures impurity effects and demonstrates localization and hydrodynamic behavior in critical many-body systems.

Findings

Localization in steady state despite macroscopic impurity separation

Vanishing energy current and uncorrelated local fluctuations

Crossover from ballistic to diffusive energy transport

Abstract

We define a simple model of conformal field theory in random space-time environments, which we refer to as stochastic conformal field theory. This model accounts for the effects of dilute random impurities in strongly interacting critical many-body systems. On one hand, surprisingly, although impurities are separated by macroscopic distances, we find that the infinite-time steady state is factorized on microscopic lengths, a signature of the emergence of localization. The stationary state also displays vanishing energy current and strong uncorrelated spatial fluctuations of local observables. On the other hand, at finite times, the transient shows a crossover from ballistic to diffusive energy propagation. In this regime and a Markovian limit, concentrating on current-generating initial states with a temperature imbalance, we show that the energy current and density satisfy simple dissipative hydrodynamic equations. We describe the space-time scales at which non-equilibrium currents exist. We show that a light-cone effect subsists in the presence of impurities although a momentum burst propagates transiently on a diffusive scale only.