Efficient Matrix Product State Method for periodic boundary conditions

TL;DR

This paper presents an improved matrix product state method for efficiently computing ground states of one-dimensional lattice models with periodic boundary conditions, significantly reducing computational effort and broadening applicability.

Contribution

It introduces a factorization technique that reduces computational complexity from m^5 to m^3 in MPS calculations for periodic systems, enhancing efficiency over previous methods.

Findings

Reduces computational effort from m^5 to m^3

Effective for S=1/2 and S=1 Heisenberg chains

Applicable to non-translationally invariant systems

Abstract

We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix Renormalization Group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from m^5 to m^3, where m is the matrix dimension, and m ~ 100 - 1000 in typical cases. We test the method on the S=1/2 and S=1 Heisenberg chains. It is also applicable to non-translationally invariant cases. The new method makes ground state calculations with periodic boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.