# Interacting invariants for Floquet phases of fermions in two dimensions

## Abstract

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.

- Authors:

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

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1571971

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 8; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Fidkowski, Lukasz, Po, Hoi Chun, Potter, Andrew C., and Vishwanath, Ashvin. Interacting invariants for Floquet phases of fermions in two dimensions. United States: N. p., 2019.
Web. doi:10.1103/physrevb.99.085115.
```

```
Fidkowski, Lukasz, Po, Hoi Chun, Potter, Andrew C., & Vishwanath, Ashvin. Interacting invariants for Floquet phases of fermions in two dimensions. United States. doi:10.1103/physrevb.99.085115.
```

```
Fidkowski, Lukasz, Po, Hoi Chun, Potter, Andrew C., and Vishwanath, Ashvin. Mon .
"Interacting invariants for Floquet phases of fermions in two dimensions". United States. doi:10.1103/physrevb.99.085115. https://www.osti.gov/servlets/purl/1571971.
```

```
@article{osti_1571971,
```

title = {Interacting invariants for Floquet phases of fermions in two dimensions},

author = {Fidkowski, Lukasz and Po, Hoi Chun and Potter, Andrew C. and Vishwanath, Ashvin},

abstractNote = {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.},

doi = {10.1103/physrevb.99.085115},

journal = {Physical Review B},

number = 8,

volume = 99,

place = {United States},

year = {2019},

month = {2}

}

*Citation information provided by*

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