Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point

Abstract

One dimensional tight binding models such as Aubry-Andre-Harper (AAH) model (with onsite cosine potential) and the integrable Maryland model (with onsite tangent potential) have been the subject of extensive theoretical research in localization studies. AAH can be directly mapped onto the two dimensional Hofstadter model which manifests the integer quantum Hall topology on a lattice. However, no such connection has been made for the Maryland model (MM). In this work, we describe a generalized model that contains AAH and MM as the limiting cases with the MM lying precisely at a topological quantum phase transition (TQPT) point. A remarkable feature of this critical point is that the 1D MM retains well defined energy gaps whereas the equivalent 2D model becomes gapless, signifying the 2D nature of the TQPT.

8 pages, 9 figures

References in corpus (7)

• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Anderson localization in Bose-Einstein condensates
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Direct measurement of topological invariants in optical lattices
• Topological equivalence of crystal and quasicrystal band structures

Cited by in corpus (15)

• Anomalous mobility edges in one-dimensional quasiperiodic models
• Dynamics and spectral theory of quasi-periodic Schrödinger-type operators
• Constructing a Weyl semimetal by stacking one dimensional topological phases
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Non-Hermitian Maryland Model
• Arithmetic Spectral Transitions for the Maryland Model
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Pure point spectrum for the Maryland model: a constructive proof
• Singular continuous spectrum for singular potential
• Maryland model in optical waveguide lattices
• Dynamical bounds for quasiperiodic Schrödinger operators with rough potentials
• Delocalization of light in photonic lattices with unbounded potentials
• Self-duality triggered dynamical transition
• Singular continuous spectrum and generic full spectral/packing dimension for unbounded quasiperiodic Schrödinger operators
• Arithmetic Phase Transitions For Mosaic Maryland Model