Gradient methods for variational optimization of projected entangled-pair states

TL;DR

This paper introduces a conjugate-gradient optimization method for ground states of projected entangled-pair states (PEPS), improving accuracy and efficiency in variational calculations for quantum many-body systems.

Contribution

It develops a robust, symmetry-compatible conjugate-gradient approach for PEPS ground-state optimization, with efficient gradient evaluation and direct computation of physical observables.

Findings

Significant energy and order parameter improvements over imaginary-time evolution methods.

Effective handling of symmetries in PEPS optimization.

Accurate computation of structure factors and Hamiltonian variance.

Abstract

We present a conjugate-gradient method for the ground-state optimization of projected entangled-pair states (PEPS) in the thermodynamic limit, as a direct implementation of the variational principle within the PEPS manifold. Our optimization is based on an efficient and accurate evaluation of the gradient of the global energy functional by using effective corner environments, and is robust with respect to the initial starting points. It has the additional advantage that physical and virtual symmetries can be straightforwardly implemented. We provide the tools to compute static structure factors directly in momentum space, as well as the variance of the Hamiltonian. We benchmark our method on Ising and Heisenberg models, and show a significant improvement on the energies and order parameters as compared to algorithms based on imaginary-time evolution.