Algorithms for entanglement renormalization

Abstract

We describe an iterative method to optimize the multiscale entanglement renormalization ansatz for the low-energy subspace of local Hamiltonians on a D -dimensional lattice. For translation-invariant systems the cost of this optimization is logarithmic in the linear system size. Specialized algorithms for the treatment of infinite systems are also described. Benchmark simulation results are presented for a variety of one-dimensional systems, namely, Ising, Potts, XX, and Heisenberg models. The potential to compute expected values of local observables, energy gaps, and correlators is investigated. © 2009 The American Physical Society.