Abstract
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 catastrophically heat to infinite temperature. We demonstrate that 1D bosonic and fermionic FSPT phases are classified by the same criteria as equilibrium phases but with an enlarged symmetry group , which now includes discrete time translation symmetry associated with the Floquet evolution. In particular, 1D bosonic FSPTs are classified by projective representations of the enlarged symmetry group . We construct explicit lattice models for a variety of systems and then formalize the classification to demonstrate the completeness of this construction. We advocate that a prototypical bosonic FSPT may be realized by very simple Hamiltonians of the type currently available in existing cold atoms and trapped ion experiments.
- Received 7 March 2016
DOI:https://doi.org/10.1103/PhysRevX.6.041001
This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Periodically shaking a quantum system (for example, by shining light on it) can completely change its properties and lead to new and potentially useful functionalities. In this way, one can endow a featureless wire with the capacity to perfectly store quantum information at its edges. Here, we develop a complete theoretical understanding of the properties of such periodically driven wires.
We develop new theoretical techniques to overcome the challenge of dealing with quantum particles that collide and interact. Such collisions and interactions are inevitably present in any real-world system but have been neglected in previous treatments. We focus on interacting symmetry-protected topological phases occurring in one dimension for both fermions and bosons. Our work reveals many new types of quantum phases of matter that would not be possible without interactions or periodic driving.
We expect that the simple models of each new phase that we construct will pave the way for experimental realization of these new phases in the laboratory.