Operator space entanglement entropy in transverse Ising chain

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.

5 pages, 2 figures (2 eps), RevTex, accepted to PRA

References in corpus (2)

• Real time evolution using the density matrix renormalization group
• Is efficiency of classical simulations of quantum dynamics related to integrability?

Cited by in corpus (5)

• Many body localization in Heisenberg XXZ magnet in a random field
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Operator Space Entanglement Entropy in XY Spin Chains
• Density Matrix Renormalization Group in the Heisenberg Picture
• Complexity of thermal states in quantum spin chains