Symmetric cluster expansions with tensor networks

Abstract

Cluster expansions for the exponential of local operators are constructed using tensor networks. In contrast to other approaches, the cluster expansion does not break any spatial or internal symmetries and exhibits a very favorable prefactor to the error scaling versus bond dimension. This is illustrated by time evolving a matrix product state using very large time steps, and by constructing a robust algorithm for finding ground states of two-dimensional Hamiltonians using projected entangled pair states as fixed points of two-dimensional transfer matrices.