Random matrix model for antiferromagnetism and superconductivity on a two-dimensional lattice

TL;DR

This paper introduces a novel mean field approach using random matrix theory to analyze the competition between antiferromagnetism and superconductivity in a two-dimensional lattice, revealing robust phase topologies.

Contribution

It develops an exact calculation method for the partition function using random matrices, linking microscopic interactions to macroscopic phase diagrams.

Findings

Phase diagram depends on a single coupling-parameter ratio, alpha.

Multiple phase topologies are robust across a broad alpha range.

The method simplifies the analysis of complex competing phases.

Abstract

We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that describe the exchange of density and spin-fluctuations. A block structure dictated by spin, time-reversal, and bipartite symmetries is imposed on the single-particle Hamiltonian. The detailed dynamics of the interactions are neglected and replaced by a normal distribution of random matrix elements. The resulting partition function can be calculated exactly. The thermodynamic potential has a structure which depends only on the spectrum of quasiparticles propagating in fixed condensation fields, with coupling constants that can be related directly to the variances of the microscopic processes. The resulting phase diagram reveals a fixed number of phase topologies whose realizations depend on a single coupling-parameter ratio, alpha. Most phase topologies are realized for a broad range of values of alpha and can thus be considered robust with respect to moderate variations in the detailed description of the underlying interactions.