Operator Space Entanglement Entropy in XY Spin Chains

TL;DR

This paper investigates the growth of operator space entanglement entropy in XY spin chains, revealing logarithmic growth dependent on the dispersion relation and phase transitions, with disorder causing saturation.

Contribution

It demonstrates that in XY spin chains, the OSEE grows at most logarithmically, with the growth rate linked to the dispersion relation's stationary points and phase transitions.

Findings

OSEE grows logarithmically in XY chains

Growth rate depends on stationary points of dispersion relation

Disorder causes saturation of OSEE

Abstract

The complexity of representation of operators in quantum mechanics can be characterized by the operator space entanglement entropy (OSEE). We show that in the homogeneous Heisenberg XY spin 1/2 chains the OSEE for initial local operators grows at most logarithmically with time. The prefactor in front of the logarithm generally depends only on the number of stationary points of the quasi-particle dispersion relation and for the XY model changes from 1/3 to 2/3 exactly at the point of quantum phase transition to long-range magnetic correlations in the non-equilibrium steady state. In addition, we show that the presence of a small disorder triggers a saturation of the OSEE.