Entanglement, decoherence and thermal relaxation in exactly solvable models

TL;DR

This paper investigates the quantum dynamics of a single spin in exactly solvable XX and XY spin chains, revealing insights into decoherence, thermalization, and finite-size effects, including stages of evolution and revivals.

Contribution

It introduces a general expression for reduced density matrix evolution in integrable models and compares decoherence and thermalization timescales, highlighting their similarity for small systems.

Findings

Decoherence and thermalization timescales are comparable for a single spin.

Finite-size effects lead to three stages: regular evolution, revivals, and chaos.

Duration of regular evolution scales with chain size.

Abstract

Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression describing the evolution of the reduced density matrix. This expression proves to be tractable when the combined closed system (i.e. open system plus environment) is integrable. Then we focus on comparing decoherence and thermalization timescales in the XX chain. We find that for a single spin these timescales are comparable, in contrast to what should be expected for a macroscopic body. This indicates that the process of quantum relaxation of a system with few accessible states can not be separated in two distinct stages - decoherence and thermalization. Finally, we turn to finite-size effects in the time evolution of a single spin in the XY chain. We observe three consecutive stages of the evolution: regular evolution, partial revivals, irregular (apparently chaotic) evolution. The duration of the regular stage is proportional to the number of spins in the chain. We observe a "quiet and cold period" in the end of the regular stage, which breaks up abruptly at some threshold time.