Self-duality triggered dynamical transition

Abstract

A basic result about the dynamics of spinless quantum systems is that the Maryland model exhibits dynamical localization in any dimension. Here we implement mathematical spectral theory and numerical experiments to show that this result does not hold, when the 2-dimensional Maryland model is endowed with spin 1/2 -- hereafter dubbed spin-Maryland (SM) model. Instead, in a family of SM models, tuning the (effective) Planck constant drives dynamical localization{delocalization transitions of topological nature. These transitions are triggered by the self-duality, a symmetry generated by some transformation in the parameter -- the inverse Planck constant -- space. This provides significant insights to new dynamical phenomena such as what occur in the spinful quantum kicked rotor.

18 pages, 6 figures

References in corpus (20)

• Floquet Topological Insulator in Semiconductor Quantum Wells
• Experimental observation of the Anderson transition with atomic matter waves
• Quantized Adiabatic Transport in Momentum Space
• Quantum Hall effect in a one-dimensional dynamical system
• Dualities and non-Abelian mechanics
• Floquet topological phases in a spin-1/2 double kicked rotor
• Controlling symmetry and localization with an artificial gauge field in a disordered quantum system
• Quantum phase transitions in the quasi-periodic kicked rotor
• Quantum simulation of disordered systems with cold atoms
• Planck's quantum-driven integer quantum Hall effect in chaos
• Dynamical many-body localization in an integrable model
• Theta renormalization, electron-electron interactions and super universality in the quantum Hall regime
• Ehrenfest time in the weak dynamical localization
• Weak dynamical localization in periodically kicked cold atomic gases
• Emergence of integer quantum Hall effect from chaos
• Sigma models for quantum chaotic dynamics
• Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point
• On the Spectrum of the Resonant Quantum Kicked Rotor
• Continuous spectrum or measurable reducibility for quasiperiodic cocycles in ${\mathbb{T}}^d\times SU(2)$
• Floquet Systems with Hall Effect: Topological Properties and Phase Transitions

Cited by in corpus (2)

• Duality,Hidden Symmetry and Dynamic Isomerism in 2D Hinge Structures
• Pseudoclassical dynamics of the kicked top