Efficient MPS algorithm for periodic boundary conditions and applications

TL;DR

This paper introduces an efficient matrix product state algorithm for one-dimensional quantum systems with periodic boundary conditions, enabling accurate calculations of spectra, ground states, and excited states for larger systems.

Contribution

It presents a novel, more efficient MPS algorithm for periodic boundary conditions, extending the applicability to larger quantum systems compared to previous methods.

Findings

Accurately computed the Haldane gap in spin-1 Heisenberg rings.

Demonstrated the algorithm's efficiency for systems with about 100 sites.

Applied the method to a mesoscopic Hubbard ring with persistent current.

Abstract

We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states (MPS), and a similar representation for Hamiltonians and other operators (MPO). It is significantly more efficient for systems of about 100 sites and more than for small quantum systems. We apply the formalism to calculate the ground state and first excited state of a spin-1 Heisenberg ring and deduce the size of the Haldane gap. The results are compared to previous high-precision DMRG calculations. Furthermore, we study spin-1 systems with a biquadratic nearest-neighbor interaction and show first results of an application to a mesoscopic Hubbard ring of spinless Fermions which carries a persistent current.