Symmetric cluster expansions with tensor networks

TL;DR

This paper introduces a symmetry-preserving tensor network-based cluster expansion method for local operators, enabling efficient time evolution and ground state computation in quantum many-body systems.

Contribution

It presents a novel tensor network approach for symmetric cluster expansions that improves error scaling and robustness in simulating quantum systems.

Findings

Efficient time evolution with large time steps using matrix product states.

A new algorithm for finding 2D ground states with projected entangled pair states.

Preservation of symmetries and favorable error scaling in the method.

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 favourable 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 novel robust algorithm for finding ground states of 2-dimensional Hamiltonians using projected entangled pair states as fixed points of 2-dimensional transfer matrices.