2024/03/27 by Kobayashi, Ryohei, Zhang, Yuxuan, Wang, Yan-Qi +1
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2403.18887
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 Gf = ℤ2f × ℤ2RT, U(1)f \rtimes ℤ2RT, and U(1)f × ℤ2RT. We show that (2+1)D invertible fermionic topological phases with these symmetries have a ℤ × ℤ8, ℤ2 × ℤ2, and ℤ2 × ℤ4 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 Gf = U(1)f \rtimes ℤ2RT, which applies to charged fermions in a magnetic field, the non-trivial value of the ℤ2 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.