Quantum Hall effect in a one-dimensional dynamical system

Abstract

We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study the quantum Hall effect in a one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible to perform experiments on the 2D quantum Hall effect using cold atoms in a 1D optical lattice.

8 pages, 6 figures

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Topological characterization of periodically-driven quantum systems
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Quantum Walk in Position Space with Single Optically Trapped Atoms
• Exploring Topological Phases With Quantum Walks
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Critical exponent for the quantum Hall transition
• Disorder-Induced Multiple Transition involving Z2 Topological Insulator
• Mesoscopic Spin Hall Effect
• Quantum phase transitions in the quasi-periodic kicked rotor
• Stroboscopic model of transport through a quantum dot with spin-orbit scattering

Cited by in corpus (68)

• Topological States and Adiabatic Pumping in Quasicrystals
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• Tunable Weyl Points in Periodically Driven Nodal Line Semimetals
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Topological Floquet Spectrum in Three Dimensions via a Two-Photon Resonance
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Quantized Adiabatic Transport in Momentum Space
• Floquet topological phases in a spin-1/2 double kicked rotor
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Scattering matrix invariants of Floquet topological insulators
• Recipe for creating an arbitrary number of Floquet chiral edge states
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk
• Floquet multi-Weyl points in crossing-nodal-line semimetals
• Fibonacci optical lattices for tunable quantum quasicrystals
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Dynamical Localization of Coupled Relativistic Kicked Rotors
• Quantum simulation of disordered systems with cold atoms
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
• Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
• Classification of Floquet Statistical Distribution for Time-Periodic Open Systems
• Planck's quantum-driven integer quantum Hall effect in chaos
• Integer Quantum Magnon Hall Plateau-Plateau Transition in a Spin Ice Model
• Finite Size Scaling of the Chalker-Coddington Model
• Localisation, delocalisation, and topological transitions in disordered 2D quantum walks
• Localization length exponent in two models of quantum Hall plateau transitions
• Metallic phase of the quantum Hall effect in four-dimensional space
• Line nodes and surface Majorana flat bands in static and kicked p-wave superconducting Harper model
• Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition
• Interband Coherence Induced Correction to Adiabatic Pumping in Periodically Driven Systems
• Dissipative Floquet Majorana modes in proximity-induced topological superconductors
• Pseudorandom binary injection of levitons for electron quantum optics
• Random network models with variable disorder of geometry
• Emergence of integer quantum Hall effect from chaos
• Localization length index in a Chalker-Coddington model: a numerical study
• Disorder effects in correlated topological insulators
• Numerical evidence for marginal scaling at the integer quantum Hall transition
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Coherent back and forward scattering peaks in the quantum kicked rotor
• Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
• Keldysh approach to periodically driven systems with a fermionic bath: non-equilibrium steady state, proximity effect and dissipation
• Phase structure of 2-dimensional topological insulators by lattice strong coupling expansion
• Topological defects in Floquet systems: Anomalous chiral modes and topological invariant
• Metal--topological-insulator transition in the quantum kicked rotator with Z2 symmetry
• Quantum Hall criticality in Floquet topological insulators
• Entanglement spectrum and entropy in Floquet topological matter
• Characterization of the Quantized Hall Insulator Phase in the Quantum Critical Regime
• Andreev reflection of quantum Hall states through a quantum point contact
• Intrinsic dissipative Floquet superconductors beyond mean-field theory
• Floquet simulators for topological surface states in isolation
• Mapping the Current-Current Correlation Function Near a Quantum Critical Point
• Self-duality triggered dynamical transition
• Geometry of random potentials: Induction of 2D gravity in Quantum Hall plateau transitions
• Prethermalization and wave condensation in a nonlinear disordered Floquet system
• Composite Fermion Nonlinear Sigma Models
• Irrelevant corrections at the quantum Hall transition
• Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice
• The integer quantum Hall transition: an $S$-matrix approach to random networks
• A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces
• Superfluidity vs prethermalisation in a nonlinear Floquet system
• Elliptic mirror of the quantum Hall effect
• Properties of dissipative Floquet Majorana modes using a quantum dot
• Edge state critical behavior of the integer quantum Hall transition
• Harris-Luck criterion in the plateau transition of the Integer Quantum Hall Effect