# Classification of Interacting Topological Floquet Phases in One Dimension

@article{Potter2016ClassificationOI, title={Classification of Interacting Topological Floquet Phases in One Dimension}, author={Andrew C. Potter and Takahiro Morimoto and Ashvin Vishwanath}, journal={arXiv: Strongly Correlated Electrons}, year={2016} }

Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting fermionic and bosonic quantum systems subject to periodic driving, which we dub Floquet SPTs (FSPTs). For physical realizations of interacting FSPTs, many-body localization by disorder is a crucial ingredient, required to obtain a stable phase that does not…

## 93 Citations

Topology and localization of a periodically driven Kitaev model

- PhysicsPhysical Review B
- 2019

Periodically driven quantum many-body systems support anomalous topological phases of matter, which cannot be realized by static systems. In many cases, these anomalous phases can be many-body…

Chiral floquet phases of many-body localized bosons

- Physics
- 2016

Author(s): Po, HC; Fidkowski, L; Morimoto, T; Potter, AC; Vishwanath, A | Abstract: We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons,…

Interacting symmetry-protected topological phases out of equilibrium

- PhysicsPhysical Review Research
- 2019

The topological features of quantum many-body wave functions are known to have profound consequences for the physics of ground-states and their low-energy excitations. We describe how topology…

Topological Phases of Non-Hermitian Systems

- PhysicsPhysical Review X
- 2018

Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular…

Classification and Construction of Topological Phases of Quantum Matter

- Physics
- 2019

We develop a theoretical framework for the classification and construction of symmetry protected topological (SPT) phases, which are a special class of zero-temperature phases of strongly interacting…

Gauging spatial symmetries and the classification of topological crystalline phases

- Mathematics
- 2016

We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what…

Fixed Points and Dynamic Topological Phenomena in a Parity-Time-Symmetric Quantum Quench

- PhysicsiScience
- 2019

Topological edge modes without symmetry in quasiperiodically driven spin chains

- PhysicsPhysical Review B
- 2022

We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology.…

Floquet quantum criticality

- PhysicsProceedings of the National Academy of Sciences
- 2018

Significance Periodically driven “Floquet” systems are nonequilibrium systems whose time translation symmetry can give rise to a rich dynamical phase structure. In the presence of quenched disorder,…

Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases

- Physics
- 2021

In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven (1+1) dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble…

## References

SHOWING 1-10 OF 61 REFERENCES

Classification of topological phases in periodically driven interacting systems

- Mathematics
- 2016

We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry $G$. We argue for a general correspondence between such phases and…

Topological Phases of One-Dimensional Fermions: An Entanglement Point of View

- Physics
- 2011

The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional…

Interacting fermionic topological insulators/superconductors in three dimensions

- Physics
- 2014

Symmetry protected topological (SPT) phases are a minimal generalization of the concept of topological insulators to interacting systems. In this paper, we describe the classification and properties…

Topological phases of fermions in one dimension

- Physics
- 2011

In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the…

Topological Characterization of Periodically-Driven Quantum Systems

- Physics
- 2010

Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also…

Effects of Disorder on a 1-D Floquet Symmetry Protected Topological Phase

- Physics
- 2015

Periodically driven systems, also known as Floquet systems, can realize symmetry protected topological (SPT) phases that cannot be found in equilibrium. Here, we seek to understand the effects of…

Protection of topological order by symmetry and many-body localization

- Physics
- 2015

In closed quantum systems, strong randomness can localize many-body excitations, preventing ergodicity. An interesting consequence is that high energy excited states can exhibit quantum coherent…

Complete classification of one-dimensional gapped quantum phases in interacting spin systems

- Physics
- 2011

Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site…

Chiral symmetry and bulk{boundary correspondence in periodically driven one-dimensional systems

- Physics
- 2014

In periodically driven lattice systems, the effective (Floquet) Hamiltonian can be engineered to be topological; then, the principle of bulk-boundary correspondence guarantees the existence of robust…

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

- PhysicsScience
- 2012

Just as group theory allows us to construct 230 crystal structures in three-dimensional space, group cohomology theory is used to systematically construct different interacting bosonic SPT phases in any dimension and with any symmetry, leading to the discovery of bosonic topological insulators and superconductors.