Carolyn Zhang, Tobias Holder, Netanel H. Lindner, Mark Rudner, Erez Berg
SciPost Phys. 12, 124 (2022) ·
published 11 April 2022
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Two-dimensional periodically driven systems can host an unconventional
topological phase unattainable for equilibrium systems, termed the Anomalous
Floquet-Anderson insulator (AFAI). The AFAI features a quasi-energy spectrum
with chiral edge modes and a fully localized bulk, leading to non-adiabatic but
quantized charge pumping. Here, we show how such a Floquet phase can be
realized in a driven, disordered Quantum Anomalous Hall insulator, which is
assumed to have two critical energies where the localization length diverges,
carrying states with opposite Chern numbers. Driving the system at a frequency
close to resonance between these two energies localizes the critical states and
annihilates the Chern bands, giving rise to an AFAI phase. We exemplify this
principle by studying a model for a driven, magnetically doped topological
insulator film, where the annihilation of the Chern bands and the formation of
the AFAI phase is demonstrated using the rotating wave approximation. This is
complemented by a scaling analysis of the localization length for two copies of
a quantum Hall network model with a tunable coupling between them. We find that
by tuning the frequency of the driving close to resonance, the driving strength
required to stabilize the AFAI phase can be made arbitrarily small.
Frederik Nathan, Dmitry A. Abanin, Netanel H. Lindner, Erez Berg, Mark S. Rudner
SciPost Phys. 10, 128 (2021) ·
published 3 June 2021
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We uncover a new family of few-body topological phases in periodically driven fermionic systems in two dimensions.
These phases, which we term correlation-induced anomalous Floquet insulators (CIAFIs), are characterized by quantized contributions to the bulk magnetization from multi-particle correlations, and are classified by a family of integer-valued topological invariants.
The CIAFI phases do not require many-body localization, but arise in the generic situation of $k$-particle localization, where the system is localized (due to disorder) for any finite number of particles up to a maximum number, $k$.
We moreover show that, when fully many-body localized, periodically driven systems of interacting fermions in two dimensions are characterized by a quantized magnetization in the bulk, thus confirming the quantization of magnetization of the anomalous Floquet insulator.
We demonstrate our results with numerical simulations.
Tobias Gulden, Erez Berg, Mark S. Rudner, Netanel H. Lindner
SciPost Phys. 9, 015 (2020) ·
published 29 July 2020
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We investigate a mechanism to transiently stabilize topological phenomena in
long-lived quasi-steady states of isolated quantum many-body systems driven at
low frequencies. We obtain an analytical bound for the lifetime of the
quasi-steady states which is exponentially large in the inverse driving
frequency. Within this lifetime, the quasi-steady state is characterized by
maximum entropy subject to the constraint of fixed number of particles in the
system's Floquet-Bloch bands. In such a state, all the non-universal properties
of these bands are washed out, hence only the topological properties persist.
