Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard model

TL;DR

This paper demonstrates that an improved energy extrapolation technique with infinite projected entangled-pair states (iPEPS) provides highly accurate energy estimates for the 2D Hubbard model in the thermodynamic limit, outperforming many existing methods.

Contribution

The paper introduces a novel extrapolation technique based on truncation error in iPEPS, significantly enhancing energy accuracy for the 2D Hubbard model in the strongly correlated regime.

Findings

iPEPS yields lower variational energies than state-of-the-art methods.

The extrapolation technique improves energy estimates in the infinite bond dimension limit.

Results agree well with quantum Monte Carlo at half filling.

Abstract

An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for 2D wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the doped Hubbard model in the strongly correlated regime ($U/t=8$, $n=0.875$) iPEPS yields lower variational energies than state-of-the-art variational methods in the large 2D limit, which demonstrates the competitiveness of the method. In order to obtain an accurate estimate of the energy in the exact infinite $D$ limit we introduce and test an extrapolation technique based on a truncation error computed in the iPEPS imaginary time evolution algorithm. The extrapolated energies are compared with accurate quantum Monte Carlo results at half filling and with various other methods in the doped, strongly correlated regime.