Hybrid Symmetry Breaking in Classical Spin Models With Subsystem Symmetries

TL;DR

This paper explores phase transitions in classical compass models with subsystem symmetries, revealing hybrid symmetry breaking where different submanifolds exhibit distinct orderings, and characterizes these phases with subdimensional order parameters.

Contribution

It introduces the concept of hybrid symmetry breaking in classical spin models with subsystem symmetries and characterizes the resulting phases with novel order parameters.

Findings

Models exhibit hybrid symmetry breaking with different patterns in submanifolds

Phase transitions are non-standard first-order transitions

Numerical confirmation of symmetry-broken phases and their properties

Abstract

We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev Hamiltonian on a cubic lattice. We show that these models experience a hybrid symmetry breaking by which the system display distinct symmetry broken patterns in different submanifolds. For instance, the system may look magnetic within a chain or plane but nematic-like when observing from one dimensionality higher. We fully characterize the symmetry-broken phases by a set of subdimensional order parameters and confirm numerically both cases undergo a non-standard first-order phase transition. Our results provide new insights into phase transitions involving subsystem symmetries and generalize the notion of conventional spontaneous symmetry breaking.