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(2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes (2403.18887v1)

Published 27 Mar 2024 in cond-mat.str-el, cond-mat.mes-hall, hep-th, and quant-ph

Abstract: It is common in condensed matter systems for reflection ($R$) and time-reversal ($T$) symmetry to both be broken while the combination $RT$ is preserved. In this paper we study invariants that arise due to $RT$ symmetry. We consider many-body systems of interacting fermions with fermionic symmetry groups $G_f = \mathbb{Z}_2f \times \mathbb{Z}_2{RT}$, $U(1)f \rtimes \mathbb{Z}_2{RT}$, and $U(1)f \times \mathbb{Z}_2{RT}$. We show that (2+1)D invertible fermionic topological phases with these symmetries have a $\mathbb{Z} \times \mathbb{Z}_8$, $\mathbb{Z}2 \times \mathbb{Z}_2$, and $\mathbb{Z}2 \times \mathbb{Z}_4$ classification, respectively, which we compute using the framework of $G$-crossed braided tensor categories. We provide a many-body $RT$ invariant in terms of a tripartite entanglement measure, and which we show can be understood using an edge conformal field theory computation in terms of vertex states. For $G_f = U(1)f \rtimes \mathbb{Z}_2{RT}$, which applies to charged fermions in a magnetic field, the non-trivial value of the $\mathbb{Z}_2$ invariant requires strong interactions. For symmetry-preserving boundaries, the phases are distinguished by zero modes at the intersection of the reflection axis and the boundary. Additional invariants arise in the presence of translation or rotation symmetry.

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