Operator space entanglement entropy in a transverse Ising chain
Abstract
The efficiency of timedependent density matrix renormalization group methods is intrinsically connected to the rate of entanglement growth. We introduce a measure of entanglement in the space of operators and show, for a transverse Ising spin 1/2 chain, that the simulation of observables, contrary to the 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.
 Publication:

Physical Review A
 Pub Date:
 September 2007
 DOI:
 10.1103/PhysRevA.76.032316
 arXiv:
 arXiv:0706.2480
 Bibcode:
 2007PhRvA..76c2316P
 Keywords:

 03.67.Mn;
 75.10.Pq;
 02.30.Ik;
 05.50.+q;
 Entanglement production characterization and manipulation;
 Spin chain models;
 Integrable systems;
 Lattice theory and statistics;
 Quantum Physics
 EPrint:
 5 pages, 2 figures (2 eps), RevTex, accepted to PRA