Thermodynamic properties of the SO(5) theory for the antiferromagnetism and d-wave superconductivity: a Monte Carlo study

TL;DR

This study uses Monte Carlo simulations to explore the thermodynamic properties of the SO(5) theory, revealing phase boundaries, hysteresis, and coexistence phenomena in antiferromagnetism and d-wave superconductivity under thermal fluctuations and external fields.

Contribution

It provides a comprehensive Monte Carlo analysis of the thermodynamics and phase transitions in the SO(5) model, including effects of external magnetic fields and flux-line lattice behavior.

Findings

Phase boundaries merge tangentially at the bicritical point.

Hysteresis observed at the AF/SC phase transition.

Coexistence of long-range SC and AF order at intermediate fields.

Abstract

The present approach takes into account thermal fluctuations both in the rotation of SO(5) superspins between the AF and SC subspaces, and in the phase variables of SC order parameters. Temperature vs. g-field phase diagrams for null external magnetic field are presented, where the g field is conjugate with the quadratic order parameters and breaks the SO(5) symmetry. The normal(N)/AF and N/SC phase boundaries merge tangentially at the bicritical point into the AF/SC phase boundary. Hysteresis phenomenon is observed at the AF/SC phase transition. Enhancement of AF correlations is observed above the SC critical temperature in systems with AF couplings stronger than SC ones. Its relation with the spin-gap phenomenon is addressed. The SO(5) theory in an external magnetic field is also investigated. At sufficiently large g fields the SC order is established through a first-order freezing transition of the flux-line lattice. Short-range AF fluctuations are larger at cores of flux lines than elsewhere, and decrease continuously to zero with increasing g field. At intermediate g fields, the flux-line lattice of long-range SC order and the long-range AF order coexist. Superlattice spots surrounding the strong AF Bragg peaks at Q=(\pm\pi,\pm\pi) are observed in the simulated structure factor, and are identified with the modulation by the triangular flux-line lattice of SC. The AF phase boundary associated with the continuous onset of long-range AF order drops sharply to the g axis from a finite temperature in the temperature vs. g-field phase diagram.