A Solution of the Hubbard Model

TL;DR

This paper presents a numerical variational approach combining tensor network states and time-evolving block decimation to solve the ground state of the two-dimensional fermionic Hubbard model, capturing key physical effects.

Contribution

It introduces a novel numerical method for solving the 2D Hubbard model's ground state using tensor networks and TEBD, handling fermion exchange and lattice size effects.

Findings

Determined ground-state energy per site as a function of chemical potential.

Observed saturation of ground-state energy with increasing lattice size.

Handled fermion exchange effects in the model.

Abstract

We report a ground-state solution for the two-dimensional fermionic Hubbard model, which is obtained via a numerical variational method. The two ingredients in this approach are tensor network states and the time-evolving block decimation. We easily handle the horizontal hopping in the Hamiltonian, and we proceed further to observe the fermion-exchange effect caused by the vertical hopping. By requiring no divergence and no convergence to zero for the ground state, we successively determine the ground-state energy per site as a function of the chemical potential and the lattice length. In addition, we observe saturation in the behavior of the ground-state energy as the lattice length increases.