Symmetry constrained field theories for chiral spin liquid to spin crystal transitions

TL;DR

This paper develops a theoretical framework using symmetry constraints and topological invariants to understand phase transitions from a chiral spin liquid to various spin crystal states, including explicit field theories for these transitions.

Contribution

It introduces a symmetry-based approach to identify topological invariants and constructs explicit Chern-Simons-matter field theories for direct transitions from a chiral spin liquid to specific spin crystal orders.

Findings

Derived compatibility conditions for topological invariants and lattice symmetries.

Constructed explicit field theories for transitions to octahedral and tetrahedral spin crystals.

Discussed extensions to broader magnetic ordering transitions.

Abstract

We consider the spin rotationally invariant Kalmeyer-Laughlin chiral spin liquid (CSL) in systems with broken time-reversal symmetry and explore symmetry constraints on possible conventional spin crystal states accessible via a direct transition. These constraints provide a framework to identify topological invariants of the magnetically ordered state. We show that the existence of a direct transition from a CSL requires a precise compatibility condition between the topological invariants of the ordered state and the anomaly of the CSL. The lattice symmetries also constrain the functional form of the low-energy theory to describe these transitions. This allows us to construct explicit Chern-Simons-matter field theories for the transition into a class of noncoplanar orders identified as candidates directly accessible from the CSL, including the octahedral spin crystal on the kagom\'e lattice, and the tetrahedral order on the triangular and honeycomb lattice. These transitions can either be described using coupled fractionalized $ \mathbb{CP}^1 $ theories or fractionalized matrix principal chiral models. We also discuss extensions to more general magnetic ordering transitions out of the CSL.