Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions

TL;DR

This paper characterizes weakly first-order phase transitions in three-dimensional spin-one quantum magnets using Poisson-Dirichlet distributions and quantum Monte Carlo, revealing the non-continuous nature of nematic state melting.

Contribution

It introduces a quantitative approach combining Poisson-Dirichlet distributions with Monte Carlo simulations to analyze weakly first-order transitions in spin-nematic systems.

Findings

Weakly first-order transition identified in nematic melting.

Exact results for order parameter distribution and Binder cumulants.

Thermal melting of spin-nematic states is a generic quantum phenomenon.

Abstract

We provide a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions (PD) within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead a weakly first-order transition is identified from both thermal properties and the distribution of the nematic order parameter. Furthermore, based on PD calculations, we obtain exact results for the order parameter distribution and Binder cumulants at the discontinuous melting transition. Our findings establish the thermal melting of planar spin-nematic states as a generic platform for quantitative approaches to weakly first-order phase transitions in quantum systems with a continuous SU(2) internal symmetry.