Nonlocality of Deep Thermalization

TL;DR

This paper investigates how the global topology of a quantum system influences the speed of deep thermalization, revealing that boundary conditions significantly affect the rate at which a local subsystem reaches a maximally-entropic state.

Contribution

It analytically and numerically demonstrates the impact of boundary conditions on deep thermalization rates in maximally-chaotic (1+1)d systems, highlighting nonlocal effects beyond standard thermalization.

Findings

Deep thermalization occurs exponentially fast with both boundary conditions.

Open boundaries slow the process by a factor of two compared to periodic boundaries.

Analytical results are supported by extensive numerical simulations.

Abstract

We study the role of global system topology in governing deep thermalization, the relaxation of a local subsystem towards a maximally-entropic, uniform distribution of post-measurement states, upon observing the complementary subsystem in a local basis. Concretely, we focus on a class of (1+1)d systems exhibiting 'maximally-chaotic' dynamics, and consider how the rate of the formation of such a universal wavefunction distribution depends on boundary conditions of the system. We find that deep thermalization is achieved exponentially quickly in the presence of either periodic or open boundary conditions; however, the rate at which this occurs is twice as fast for the former than for the latter. These results are attained analytically using the calculus of integration over unitary groups, and supported by extensive numerical simulations. Our findings highlight the nonlocal nature of deep thermalization, and clearly illustrates that the physics underlying this phenomenon goes beyond that of standard quantum thermalization, which only depends on the net build-up of entanglement between a subsystem and its complement.