Post-Quantum Quench Growth of Renyi Entropies in Low Dimensional Continuum Bosonic Systems

TL;DR

This paper introduces a simulation method to analyze the growth of Renyi entropies in low-dimensional bosonic systems after energy injection, applicable to complex interacting models like sine-Gordon, revealing entanglement dynamics over time.

Contribution

We develop a novel simulation scheme for Renyi entropy growth in Luttinger liquids with arbitrary interactions, including gapped systems, and apply it to the sine-Gordon model.

Findings

Analytic expressions for short-time Renyi entropy growth

Simulation scheme effective for complex interacting systems

Insights into entanglement dynamics post-quench

Abstract

The growth of Renyi entropies after the injection of energy into a correlated system provides a window upon the dynamics of its entanglement properties. We develop here a simulation scheme by which this growth can be determined in Luttinger liquids systems with arbitrary interactions, even those introducing gaps into the liquid. We apply this scheme to an experimentally relevant quench in the sine-Gordon field theory. While for short times we provide an analytic expression for the growth of the second and third Renyi entropy, to access longer times, we combine our scheme with truncated spectrum methods.