scholarly journals Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Frederik Nathan ◽  
Dmitry Abanin ◽  
Netanel Lindner ◽  
Erez Berg ◽  
Mark Spencer Rudner
Keyword(s):  
Two Dimensions ◽  
Topological Invariants ◽  
Many Body ◽  
Driven Systems ◽  
Periodically Driven ◽  
New Family ◽  
Fermionic Systems ◽  
Bulk Magnetization ◽  
Particle Localization ◽  
Number Of Particles

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.

scholarly journals Theory of many-body localization in periodically driven systems

2016 ◽  
Vol 372 ◽  
pp. 1-11 ◽  
Author(s):  
Dmitry A. Abanin ◽  
Wojciech De Roeck ◽  
François Huveneers
Keyword(s):  
Many Body ◽  
Driven Systems ◽  
Periodically Driven

scholarly journals Absence of dynamical localization in interacting driven systems

2017 ◽  
Vol 3 (4) ◽  
Author(s):  
David J. Luitz ◽  
Yevgeny Bar Lev ◽  
Achilleas Lazarides
Keyword(s):  
Diffusion Coefficient ◽  
Weak Interactions ◽  
Interaction Strength ◽  
Dynamical Localization ◽  
Driven Systems ◽  
Periodically Driven ◽  
Diffusive Regime ◽  
The Stability ◽  
Small Interactions ◽  
Number Of Particles

Using a numerically exact method we study the stability of dynamical localization to the addition of interactions in a periodically driven isolated quantum system which conserves only the total number of particles. We find that while even infinitesimally small interactions destroy dynamical localization, for weak interactions density transport is significantly suppressed and is asymptotically diffusive, with a diffusion coefficient proportional to the interaction strength. For systems tuned away from the dynamical localization point, even slightly, transport is dramatically enhanced and within the largest accessible systems sizes a diffusive regime is only pronounced for sufficiently small detunings.

scholarly journals Magnus Expansion Approach to Parametric Oscillator Systems in a Thermal Bath

2016 ◽  
Vol 71 (10) ◽  
pp. 921-932 ◽  
Author(s):  
Beilei Zhu ◽  
Tobias Rexin ◽  
Ludwig Mathey
Keyword(s):  
Parametric Instability ◽  
Parametric Oscillator ◽  
Dissipative Systems ◽  
Thermal Bath ◽  
Driving Frequency ◽  
Many Body ◽  
Magnus Expansion ◽  
Driven Systems ◽  
Oscillator Frequency ◽  
Periodically Driven

AbstractWe develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and in the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving term with a cosine dependence on time, up to fourth order. We apply these to the steady state of a classical parametric oscillator coupled to a thermal bath, which we solve numerically for comparison. Beyond dynamical stabilisation at second order, we find that the higher orders further renormalise the oscillator frequency, and additionally create a weakly renormalised effective temperature. The renormalised oscillator frequency is quantitatively accurate almost up to the parametric instability, as we confirm numerically. Additionally, a cut-off dependent term is generated, which indicates the break down of the hierarchy of time scales of the system, as a precursor to the instability. Finally, we apply this formalism to a parametrically driven chain, as an example for the control of the dispersion of a many-body system.

scholarly journals Many-Body Localization in Periodically Driven Systems

2015 ◽  
Vol 114 (14) ◽  
Author(s):  
Pedro Ponte ◽  
Z. Papić ◽  
François Huveneers ◽  
Dmitry A. Abanin
Keyword(s):  
Many Body ◽  
Driven Systems ◽  
Periodically Driven

scholarly journals Anatomy of a Periodically Driven p-Wave Superconductor

2016 ◽  
Vol 71 (10) ◽  
pp. 883-895 ◽  
Author(s):  
Erhai Zhao
Keyword(s):  
Two Dimensions ◽  
P Wave ◽  
Edge States ◽  
Many Body ◽  
Simple Description ◽  
Periodically Driven ◽  
Topological Superconductors ◽  
Many Body Systems ◽  
Isolated Point ◽  
Topological Singularities

AbstractThe topological properties of periodically driven many-body systems often have no static analogs and defy a simple description based on the effective Hamiltonian. To explore the emergent edge modes in driven p-wave superconductors in two dimensions, we analysed a toy model of Kitaev chains (one-dimensional spinless p-wave superconductors with Majorana edge states) coupled by time-periodic hopping. We showed that with proper driving, the coupled Kitaev chains can turn into a fully gapped superconductor, which is analogous to the px+ipy state but has two, rather than one, chiral edge modes. A different driving protocol turns it into a gapless superconductor with isolated point nodes and completely flat edge states at quasienergy ω=0 or π/T, with T as the driving period. The time evolution operator U(kx, ky, t) of the toy model is computed exactly to yield the phase bands. And the “topological singularities” of the phase bands are exhausted and compared to those of a periodically driven Hofstadter model, which features counter-propagating chiral edge modes. These examples demonstrate the unique edge states in driven superconducting systems and suggest driving as a potentially fruitful route to engineer new topological superconductors.

Transport of quantum states of periodically driven systems

1990 ◽  
Vol 51 (8) ◽  
pp. 709-722 ◽  
Author(s):  
H.P. Breuer ◽  
K. Dietz ◽  
M. Holthaus
Keyword(s):  
Quantum States ◽  
Driven Systems ◽  
Periodically Driven

scholarly journals Fine structures of valley-polarized excitonic states in monolayer transitional metal dichalcogenides

Nanophotonics ◽  
2020 ◽  
Vol 9 (7) ◽  
pp. 1811-1829 ◽  
Author(s):  
Zhipeng Li ◽  
Tianmeng Wang ◽  
Shengnan Miao ◽  
Zhen Lian ◽  
Su-Fei Shi
Keyword(s):  
Optical Excitation ◽  
Coherence Time ◽  
Two Dimensions ◽  
Degree Of Freedom ◽  
Research Progress ◽  
Many Body ◽  
Transitional Metal ◽  
Metal Dichalcogenides ◽  
Fine Structures ◽  
Excitonic States

AbstractMonolayer transitional metal dichalcogenides (TMDCs), a new class of atomically thin semiconductor, respond to optical excitation strongly with robust excitons, which stem from the reduced screening in two dimensions. These excitons also possess a new quantum degree of freedom known as valley spin, which has inspired the field of valleytronics. The strongly enhanced Coulomb interaction allows the exciton to bind with other particles to form new excitonic states. However, despite the discovery of trions, most of the excitonic states in monolayer TMDCs remain elusive until recently, when new light was shed into the fascinating excitonic fine structures with drastically improved sample quality through boron nitride encapsulation. Here, we review the latest research progress on fine structures of excitonic states in monolayer TMDCs, with a focus on tungsten-based TMDCs and related alloy. Many of the new excitonic complexes inherit the valley degree of freedom, and the valley-polarized dark excitonic states are of particular interest because of their long lifetime and possible long valley coherence time. The capability of resolving the excitonic fine structures also enables the investigation of exciton–phonon interactions. The knowledge of the interlayer between excitons and other particles not only advances our understanding of many-body effects in the monolayer TMDCs but also provides guidance on future applications based on TMDCs.

Noise-induced transitions between attractors in time periodically driven systems

1992 ◽  
Vol 68 (25) ◽  
pp. 3670-3673 ◽  
Author(s):  
Olaf Stiller ◽  
Andreas Becker ◽  
Lorenz Kramer
Keyword(s):  
Driven Systems ◽  
Periodically Driven
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