Operator space entanglement entropy in transverse Ising chain

TL;DR

This paper introduces a new measure of operator space entanglement entropy in the transverse Ising chain, revealing that the simulation efficiency depends on the initial operator's properties, with entropy saturation or logarithmic growth.

Contribution

It defines operator space entanglement entropy and analyzes its growth, showing efficient simulation for certain initial operators in the transverse Ising model.

Findings

Operator space entanglement entropy saturates for finite index initial operators.

Logarithmic growth of entanglement entropy for infinite index initial operators.

Analytical calculation of entropy saturation levels.

Abstract

The efficiency of time dependent density matrix renormalization group methods is intrinsically connected with the rate of entanglement growth. We introduce a new measure of entanglement in the space of operators and show, for transverse Ising spin 1/2 chain, that the simulation of observables, contrary to simulation of typical pure quantum states, is efficient for initial local operators. For initial operators with a finite index in Majorana representation, the operator space entanglement entropy saturates with time to a level which is calculated analytically, while for initial operators with infinite index the growth of operator space entanglement entropy is shown to be logarithmic.