Finite Projected Entangled Pair States for the Hubbard model

TL;DR

This paper develops and optimizes a finite PEPS algorithm with symmetry considerations for the 2D Hubbard model, demonstrating its effectiveness on lattices up to 8x8.

Contribution

It introduces a PEPS algorithm incorporating SU(2) symmetry and compares optimization schemes for the 2D Hubbard model on finite lattices.

Findings

Effective optimization of fPEPS for 8x8 lattices

Incorporation of SU(2) symmetry improves efficiency

Comparison of local and gradient-based optimization methods

Abstract

We adapt and optimize the projected-pair-entangled-state (PEPS) algorithm on finite lattices (fPEPS) for two-dimensional Hubbard models and apply the algorithm to the Hubbard model with nearest-neighbor hopping on a square lattice. In particular, we formulate the PEPS algorithm using projected entangled pair operators, incorporate SU(2) symmetry in all tensor indices, and optimize the PEPS using both iterative-diagonalization-based local bond optimization and gradient-based optimization of the PEPS. We discuss the performance and convergence of the algorithm for the Hubbard model on lattice sizes of up to 8x8 for PEPS states with U(1) symmetric bond dimensions of up to D = 8 and SU(2) symmetric bond dimensions of up to D = 6. Finally, we comment on the relative and overall efficiency of schemes for optimizing fPEPS.