Matrix product operator representations

TL;DR

This paper develops methods to construct matrix product operators for various dimensions and interactions, enabling advanced simulations of quantum systems with long-range interactions.

Contribution

It introduces new techniques for building translationally invariant matrix product operators applicable to complex Hamiltonians.

Findings

Constructed matrix product operators for higher dimensions.

Demonstrated applicability to long-range interacting Hamiltonians.

Enabled new algorithms for quantum spin system simulations.

Abstract

We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular, we construct translational invariant matrix product operators suitable for time evolution, and show how such descriptions are possible for Hamiltonians with long-range interactions. We illustrate how those tools can be exploited for constructing new algorithms for simulating quantum spin systems.