Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States

TL;DR

This paper introduces a finite-size fermionic tensor network method combined with variational Monte Carlo to accurately simulate the 2D Hubbard model's ground state, surpassing previous state-of-the-art energies on large lattices.

Contribution

The authors develop a novel approach using finite-size fermionic projected entangled pair states with variational Monte Carlo, achieving higher accuracy than existing methods for large 2D Hubbard lattices.

Findings

Surpassed state-of-the-art DMRG energies on 8-leg ladders.

Achieved accurate ground-state energies on large 2D lattices.

Observed the dimensional crossover between stripe orientations at specific doping.

Abstract

We demonstrate the use of finite-size fermionic projected entangled pair states, in conjunction with variational Monte Carlo, to perform accurate simulations of the ground-state of the 2D Hubbard model. Using bond dimensions of up to $D=28$, we show that we can surpass state-of-the-art DMRG energies that use up to $m=32000$ SU(2) multiplets on 8-leg ladders. We further apply our methodology to $10\times 16$, $12\times 16$ and $16 \times 16$ lattices at $1/8$ hole doping and observe the dimensional crossover between stripe orientations. Our work shows the power of finite-size fermionic tensor networks to resolve the physics of the 2D Hubbard model and related problems.