Pseudospin SU(2) Symmetry Breaking, Charge Density Wave and Superconductivity in the Hubbard Model

TL;DR

This paper explores how breaking pseudospin SU(2) symmetry in the negative-U Hubbard model leads to charge density waves and superconductivity, revealing their coexistence and mutual influence.

Contribution

It demonstrates the physical consequences of pseudospin symmetry breaking, including the emergence of CDW and superconducting phases, and their coexistence as a supersolid state.

Findings

Pseudospin symmetry breaking induces charge density wave ground states.

Breaking U(1) symmetry leads to superconductivity with off-diagonal long-range order.

Charge density wave suppresses but does not eliminate superconductivity.

Abstract

In this paper, we discuss physical consequences of pseudospin SU(2) symmetry breaking in the negative-U Hubbard model at half-filling. If pseudospin symmetry is spontaneously broken while its unique subgroup U(1) remains invariant, it will lead to the charge density wave (CDW) ground state. Furthermore, if the U(1) symmetry is also broken, the ground state will have the off-diagonal long range order (ODLRO), signaling a superconductor. In this case, CDW and superconductivity coexist to form a supersolid. Finally, we show that CDW suppresses, but does not destroy superconductivity.