Entanglement Entropy dynamics in Heisenberg chains

TL;DR

This paper investigates the time evolution of entanglement entropy in Heisenberg chains after a sudden change in anisotropy, revealing linear growth in clean systems and logarithmic growth indicating localization in disordered systems.

Contribution

It provides a detailed analysis of entanglement dynamics in Heisenberg chains using DMRG, comparing clean and disordered cases and relating results to conformal field theory.

Findings

Linear entropy growth in clean chains

Saturation of entropy after initial increase

Logarithmic growth indicating localization in disordered chains

Abstract

By means of the time-dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyze the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare, wherever possible, our results with those obtained by means of Conformal Field Theory. In the disordered case we find a slower (logarithmic) evolution which may signals the onset of entanglement localization.