Excitations and the tangent space of projected entangled-pair states

TL;DR

This paper introduces tangent space methods for PEPS to analyze low-energy excitations in 2D quantum systems, enabling direct computation of spectral properties and gaps in the thermodynamic limit.

Contribution

It presents a novel variational ansatz for elementary excitations on PEPS, allowing efficient calculation of spectral features in strongly-correlated 2D quantum models.

Findings

Computed magnon spectra for the AKLT model.

Analyzed anyonic excitations in perturbed toric code.

Demonstrated efficient correlation function evaluations.

Abstract

We develop tangent space methods for projected entangled-pair states (PEPS) that provide direct access to the low-energy sector of strongly-correlated two-dimensional quantum systems. More specifically, we construct a variational ansatz for elementary excitations on top of PEPS ground states that allows for computing gaps, dispersion relations, and spectral weights directly in the thermodynamic limit. Solving the corresponding variational problem requires the evaluation of momentum transformed two-point and three-point correlation functions on a PEPS background, which we can compute efficiently by using a contraction scheme. As an application we study the spectral properties of the magnons of the Affleck-Kennedy-Lieb-Tasaki model on the square lattice and the anyonic excitations in a perturbed version of Kitaev's toric code.