A three-state model with competing antiferromagnetic and pairing interactions

TL;DR

This paper introduces a three-state model to simulate competing antiferromagnetic and pairing interactions, capturing key features of high-temperature superconductor phase diagrams through mean field and Monte Carlo methods.

Contribution

The paper presents a novel three-state model that captures the interplay of antiferromagnetism and pairing interactions, reproducing phase diagrams similar to high-$T_c$ superconductors.

Findings

Phase diagram shows antiferromagnetic and hole-mediated ordered phases.

Mean field approximation reproduces qualitative phase boundaries.

Monte Carlo simulations characterize phase transitions.

Abstract

Motivated by the rich phase diagram of the high temperature superconductors, we introduce a toy model with three state variables which can be interpreted as two state particles and holes. The Hamiltonian has a term which favors antiferromagnetism and an additional competing interaction which favors bonding between pairs of antiparallel spins mediated by holes. For low concentration of holes the dominant interaction between particles has antiferromagnetic character, leading to an antiferromagnetic phase in the temperature-hole concentration phase diagram, qualitatively similar to the antiferromagnetic phase of doped Mott insulators. For growing concentration of holes antiferromagnetic order is weakend and a phase with a different kind of order mediated by holes appears. This last phase has the form of a dome in the T-hole concentration plane. The whole phase diagram resembles those of some families of high $T_c$ superconductors. We compute the phase diagram in the mean field approximation and characterize the different phase transitions through Monte Carlo simulations.