Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System

TL;DR

This paper explores how the Lindblad spectrum influences the dynamics of the second Rènyi entropy in open quantum systems, revealing two energy scales that govern short- and long-term behaviors and connecting dissipation strength to entropy evolution.

Contribution

It introduces a novel analysis linking Lindblad spectrum segment structure and energy scales to the dynamics of the second Rènyi entropy in many-body quantum systems under dissipation.

Findings

Two energy scales in Lindblad spectrum determine entropy dynamics.

Short-time entropy dynamics accelerates with increased dissipation.

Long-time entropy dynamics decelerates with increased dissipation.

Abstract

In this letter we point out that the Lindblad spectrum of a quantum many-body system displays a segment structure and exhibits two different energy scales in the strong dissipation regime. One energy scale determines the separation between different segments, being proportional to the dissipation strength, and the other energy scale determines the broadening of each segment, being inversely proportional to the dissipation strength. Ultilizing a relation between the dynamics of the second R\'enyi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short- and the long-time dynamics of the second R\'enyi entropy starting from a generic initial state. This gives rise to opposite behaviors, that is, as the dissipation strength increases, the short-time dynamics becomes faster and the long-time dynamics becomes slower. We also interpret the quantum Zeno effect as specific initial states that only occupy the Lindblad spectrum around zero, for which only the broadening energy scale of the Lindblad spectrum matters and gives rise to suppressed dynamics with stronger dissipation. We illustrate our theory with two concrete models that can be experimentally verified.