An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation

TL;DR

This paper reviews recent advances in variational ground state simulations of 2D quantum systems using infinite projected entangled-pair states (iPEPS) enhanced by automatic differentiation, improving accuracy and convergence.

Contribution

It introduces a comprehensive framework for iPEPS variational optimization with automatic differentiation, including foundational theory and benchmarking results.

Findings

Automatic differentiation enables flexible variational optimization of iPEPS.

The framework improves convergence and accuracy in 2D quantum ground state simulations.

Benchmarking demonstrates the effectiveness of the proposed methods.

Abstract

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work we review the state-of-the-art of the variational iPEPS framework, providing a detailed introduction to automatic differentiation, a description of a general foundation into which various two-dimensional lattices can be conveniently incorporated, and demonstrative benchmarking results.