Higher Symmetries in Condensed Matter Physics

TL;DR

This paper explores the application of higher symmetry groups, specifically SO(n), to condensed matter systems, focusing on their role in the two-dimensional Hubbard model related to high-temperature superconductivity.

Contribution

It introduces the use of higher symmetry groups like SO(4), SO(5), SO(6), and SO(8) in analyzing the Hubbard model and its relevance to cuprate superconductors.

Findings

Higher symmetry groups can describe complex phases in condensed matter.

SO(n) groups provide new insights into high T_c superconductivity.

Application of these symmetries may lead to novel theoretical frameworks.

Abstract

We discuss some applications of higher symmetry groups to condensed matter systems. We give special attention to the groups SO(n) (n = 4, 5, 6, 8) in the two-dimensional Hubbard model and its generalizations, which model the high T_c cuprate superconductors.