Symmetric cluster expansions with tensor networks
Bram Vanhecke, Laurens Vanderstraeten, Frank Verstraete
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.
Topics & Concepts
ScalingHomogeneous spaceDimension (graph theory)Matrix multiplicationTensor productTensor (intrinsic definition)Cluster (spacecraft)MathematicsCluster expansionMatrix (chemical analysis)Exponential functionStatistical physicsPure mathematicsPhysicsMathematical analysisComputer scienceGeometryQuantum mechanicsQuantumComposite materialProgramming languageMaterials scienceQuantum many-body systemsQuantum and electron transport phenomenaQuantum Computing Algorithms and Architecture