Efficient Matrix Product State Method for periodic boundary conditions

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.

Final published version

References in corpus (4)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• DMRG and periodic boundary conditions: a quantum information perspective
• Variational quantum Monte Carlo simulations with tensor-network states
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods

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