On ground-state instability in two-dimensional antiferromagnetic systems

TL;DR

This paper investigates the instability of the antiferromagnetic ground state in two-dimensional systems, revealing its tendency to form a high-temperature superconducting condensate, especially under doping conditions.

Contribution

It introduces a non-perturbative analysis of ground-state instability in 2D antiferromagnets using Dyson--Schwinger equations, linking magnetic order to superconductivity.

Findings

Ground state is unstable for all three-point couplings.

Instability leads to formation of high-$T_C$ superconducting condensate.

Energy gap behavior aligns with high-$T_C$ superconductivity.

Abstract

We discuss the stability of the antiferromagnetic ground state in two spatial dimensions. We start with a general analysis, based on Gribov's current-conservation techniques, of the bosonic modes in systems with magnetic order. We argue that the Goldstone $\phi$ and Higgs $h$ modes mix in antiferromagnetic systems, and this leads to an effective $hh\phi$ three-point interaction. We then analyze the instability of the antiferromagnetic system in two spatial dimensions by studying the non-perturbative behaviour of the Higgs boson self-energy using the Dyson--Schwinger equations. The ground state turns out to be unstable for all values of the three-point coupling. We interpret this as being due to the formation of a (high-$T_C$) superconducting condensate. The carrier doping dependence of the energy gap has a general behaviour that is consistent with high-$T_C$ superconductivity. Superconductivity co-exists with antiferromagnetic order for large magnetization, or small doping.