Variational optimization algorithms for uniform matrix product states

摘要

We combine the Density Matrix Renormalization Group (DMRG) with MatrixProduct State tangent space concepts to construct a variational algorithm forfinding ground states of one dimensional quantum lattices in the thermodynamiclimit. A careful comparison of this variational uniform Matrix Product Statealgorithm (VUMPS) with infinite Density Matrix Renormalization Group (IDMRG)and with infinite Time Evolving Block Decimation (ITEBD) reveals substantialgains in convergence speed and precision. We also demonstrate that VUMPS worksvery efficiently for Hamiltonians with long range interactions. The newalgorithm can be conveniently implemented as an extension of an alreadyexisting DMRG implementation.