Stiffness in 1D Matrix Product States with periodic boundary conditions

TL;DR

This paper improves a variational matrix-product-state algorithm for periodic boundary conditions, enabling accurate study of large 1D quantum systems and applying it to compute the stiffness of strongly correlated models.

Contribution

It introduces enhancements to an existing MPS algorithm for periodic systems, increasing stability and reliability for large-scale quantum simulations.

Findings

Algorithm achieves higher stability and accuracy.

Successfully computes stiffness in Heisenberg chain.

Validates method against exactly solvable models.

Abstract

We discuss in details a modified variational matrix-product-state algorithm for periodic boundary conditions, based on a recent work by P. Pippan, S.R. White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to study large systems on a ring (composed of N ~ 10^2 sites). In particular, we introduce a couple of improvements that allow to enhance the algorithm in terms of stability and reliability. We employ such method to compute the stiffness of one-dimensional strongly correlated quantum lattice systems. The accuracy of our calculations is tested in the exactly solvable spin-1/2 Heisenberg chain.