Interplay of superconductivity and magnetism in strong coupling

TL;DR

This paper introduces a model exploring the complex interplay between superconductivity and magnetism, analyzing phase transitions, quantum criticality, and emergent symmetries in a strong-coupling regime with rich phase behavior.

Contribution

It presents a detailed analysis of a strong-coupling model showing how superconductivity and antiferromagnetism coexist and transition, including quantum corrections and symmetry considerations.

Findings

Rich mean-field phase diagram with first- and second-order transitions

Quantum critical behavior observed above the spin-disordering line

Emergence of SO(5) symmetry at the tricritical point

Abstract

A model is introduced describing the interplay between superconductivity and spin-ordering. It is characterized by on-site repulsive electron-electron interactions, causing antiferromagnetism, and nearest-neighbor attractive interactions, giving rise to d-wave superconductivity. Due to a special choice for the lattice, this model has a strong-coupling limit where the superconductivity can be described by a bosonic theory, similar to the strongly coupled negative U Hubbard model. This limit is analyzed in the present paper. A rich mean-field phase diagram is found and the leading quantum corrections to the mean-field results are calculated. The first-order line between the antiferromagnetic- and the superconducting phase is found to terminate at a tricritical point, where two second-order lines originate. At these lines, the system undergoes a transition to- and from a phase exhibiting both antiferromagnetic order and superconductivity. At finite temperatures above the spin-disordering line, quantum-critical behavior is found. For specific values of the model parameters, it is possible to obtain SO(5) symmetry involving the spin- and the phase-sector at the tricritical point. Although this symmetry is explicitly broken by the projection to the lower Hubbard band, it survives on the mean-field level, and modes related to a spontaneously broken SO(5) symmetry are present on the level of the random phase approximation in the superconducting phase.