Observations outside the light cone: Algorithms for nonequilibrium and thermal states
Abstract
We apply algorithms based on LiebRobinson bounds to simulate timedependent and thermal quantities in quantum systems. For timedependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of “observing” the system outside the light cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to a very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light cone naturally matches the LiebRobinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain as compared to a direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on onedimensional systems with mixed ferromagnetic and antiferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.
 Publication:

Physical Review B
 Pub Date:
 April 2008
 DOI:
 10.1103/PhysRevB.77.144302
 arXiv:
 arXiv:0801.2161
 Bibcode:
 2008PhRvB..77n4302H
 Keywords:

 03.67.Mn;
 02.70.c;
 05.50.+q;
 75.10.Pq;
 Entanglement production characterization and manipulation;
 Computational techniques;
 simulations;
 Lattice theory and statistics;
 Spin chain models;
 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 19 pages, 12 figures