Global SO(3)×SO(3)×U(1) symmetry of the Hubbard model on bipartite lattices

12Citations
Citations of this article
4Readers
Mendeley users who have this article in their library.
Get full text

Abstract

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U≠0 the local SU(2)×SU(2)×U(1) gauge symmetry of the Hubbard model on a bipartite lattice with NaD sites and vanishing transfer integral t=0 can be lifted to a global [SU(2)×SU(2)×U(1)]/Z22=SO(3)×SO(3)×U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t>0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L=Na a for which D=1, 2, 3,... in the number NaD of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4NaD energy eigenstates refer to representations of the new found global [SU(2)×SU(2)×U(1)]/Z22=SO(3)×SO(3)×U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3)×SO(3)×U(1) equals the Hilbert-space dimension 4NaD. It is confirmed elsewhere that the new found symmetry has important physical consequences. © 2010 Elsevier Inc.

Cite

CITATION STYLE

APA

Carmelo, J. M. P., Östlund, S., & Sampaio, M. J. (2010). Global SO(3)×SO(3)×U(1) symmetry of the Hubbard model on bipartite lattices. Annals of Physics, 325(8), 1550–1565. https://doi.org/10.1016/j.aop.2010.03.002

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free