Classification of phase transitions and intertwined orders in crystallographic point groups

TL;DR

This paper uses group theory to classify phase transitions and intertwined orders in all 32 crystallographic point groups, providing a framework to understand symmetry-breaking phenomena and predict transition characteristics.

Contribution

It offers a comprehensive group-theoretical classification of intertwined orders and phase transitions across all crystallographic point groups, linking symmetries to order parameters and transition types.

Findings

Unique determination of order parameter irreps from symmetries

Classification of possible intertwined orders in each point group

Predictive framework for phase transition nature and emergent symmetries

Abstract

Symmetry provides important insight in understanding the nature of phase transitions. In the presence of crystalline symmetries, new phenomena in phase transition can emerge, such as intertwined orders and emergent symmetries. In this work, we present a group-theoretical diagnosis of these phenomena in 32 crystallographic point groups. For each group, we classify the possible combinations of intertwined order and analyze different symmetry-broken phases. We find that the symmetries before and after the phase transition uniquely determine the irreducible representation (irrep) of the order parameter and the allowed form of Ginzburg-Landau free energy, from which the nature of phase transition can be inferred, including the order of phase transition and the existence of intermediate phases and emergent symmetries. Our finding will be helpful for the experimental diagnosis of order parameters from symmetry breaking.