Interacting invariants for Floquet phases of fermions in two dimensions

Journal Article · 11 February 2019 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.99.085115 · OSTI ID:1571971

Fidkowski, Lukasz ^[1]; Po, Hoi Chun ^[2]; Potter, Andrew C. ^[3]; Vishwanath, Ashvin ^[2]

---

1. Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
2. Univ. of California, Berkeley, CA (United States). Dept. of Physics; Harvard Univ., Cambridge, MA (United States). Dept. of Physics
3. Univ. of Texas, Austin, TX (United States). Dept. of Physics

We construct a many-body quantized invariant that sharply distinguishes among two-dimensional nonequilibrium driven phases of interacting fermions. This is an interacting generalization of a band-structure Floquet quasienergy winding number and describes chiral pumping of quantum information along the edge. In particular, our invariant sharply distinguishes between a trivial and anomalous Floquet Anderson insulator in the interacting, many-body localized setting. It also applies more generally to models where only fermion parity is conserved, where it differentiates between trivial models and ones that pump Kitaev Majorana chains to the boundary, such as ones recently introduced in the context of emergent fermions arising from eigenstate $$ \mathbb{Z}_2$$ topological order. We evaluate our invariant for the edge of such a system with eigenstate $$ \mathbb{Z}_2$$ topological order, and show that it is necessarily nonzero when the Floquet unitary exchanges electric and magnetic excitations, proving a connection between bulk anyonic symmetry and edge chirality that was recently conjectured.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1571971
• Journal Information: Physical Review. B, Vol. 99, Issue 8; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English