Applying matrix product operators to model systems with long-range interactions

TL;DR

This paper introduces a novel algorithm that uses matrix product operators to efficiently model and compute ground states of 1D systems with long-range interactions, demonstrated on the Haldane-Shastry model.

Contribution

The paper presents a new method combining matrix product states and operators to handle long-range interactions in infinite 1D systems.

Findings

Successfully computed ground state of the Haldane-Shastry model

Able to model any long-range interaction approximated by decaying exponentials

Provides an efficient approach for infinite 1D systems with long-range interactions

Abstract

An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite 1D system; it does this by embedding sites into an approximation of the infinite ``environment'' of the chain, allowing the sites to relax, and then merging them with the environment in order to refine the approximation. By making use of matrix product operators, our approach is able to directly model any long-range interaction that can be systematically approximated by a series of decaying exponentials. We apply our techniques to compute the ground state of the Haldane-Shastry model and present results.