Automatic differentiation applied to excitations with Projected Entangled Pair States

TL;DR

This paper introduces a method to optimize excitation states in tensor network simulations using automatic differentiation, demonstrating its effectiveness on the Hubbard model in two dimensions.

Contribution

It extends automatic differentiation techniques to the excitation ansatz in tensor networks, enabling more accurate and simpler optimization of quasiparticle excitations in 2D systems.

Findings

Effective reimplementation of excitation optimization with automatic differentiation.

Successful application to the 2D Hubbard model at half filling.

Improved accuracy and simplicity in excitation state calculations.

Abstract

The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the two-dimensional tensor network class of infinite entangled pair states gained new ground state optimization methods based on automatic differentiation, which are at the same time highly accurate and simple to implement. Naturally, the question arises whether these new ideas can also be used to optimize the excitation ansatz, which has recently been implemented in two dimensions as well. In this paper, we describe a straightforward way to reimplement the framework for excitations using automatic differentiation, and demonstrate its performance for the Hubbard model at half filling.