A Solution of the Hubbard Model

2013/11/21 by Myung-Hoon Chung, Chung, Myung-Hoon
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el)

paper · pdf · doi:10.48550/arxiv.1311.5300

openalex publication_date 2013/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The renormalization group: Critical phenomena and the Kondo problem
• Electron correlations in narrow energy bands

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