Diffusion and signatures of localization in stochastic conformal field theory

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.

5 pages + 4 pages suppl. mat., 2 figures. V2: discussion improved

References in corpus (4)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Spin diffusion from an inhomogeneous quench in an integrable system
• Conservation laws, integrability and transport in one-dimensional quantum systems

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