The general approach to the critical phase with coupled quasiperiodic chains

Abstract

In disordered systems, wave functions in the Schrödinger equation may exhibit a transition from the extended phase to the localized phase, in which the states at the boundaries or mobility edges may exhibit multifractality. Meanwhile, the Critical Phase (CP), where all states exhibit multifractal structures, has also attracted much attention in the past decades. However, a generic way to construct the CP on demand still remains elusive. Here, a general approach for this phase is presented using two coupled quasiperiodic chains, where the chains are chosen so that before coupling one of them has extended states while the other one has localized states. We demonstrate the existence of CP in the overlapped spectra in the presence of inter-chain coupling using fractal dimension and minimal scaling index based on multifractal analysis. Then we examine the generality of this physics by changing the forms of inter-chain coupling and quasiperiodic potential, where the CP also emerges in the overlapped spectra. We account for the emergence of this phase as a result of effective unbounded potential, which yields singular continuous spectra and excludes the extended states in the overlapped regimes. Finally, the realization of this CP in the continuous model using ultracold atoms with bichromatic incommensurate optical lattice is also discussed. Due to the tunability of the two chains, this work provides a general approach to realizing the CP in a tunable way. This approach may have wide applications in the experimental detection of CP and can be generalized to much more intriguing physics in the presence of interaction for the many-body CP.

23 pages, 17 figures

References in corpus (16)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Exact relations between multifractal exponents at the Anderson transition
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Spin-dependent Optical Superlattice
• Lyapunov exponent, mobility edges, and critical region in the generalized Aubry-Andre model with an unbounded quasiperiodic potential
• Multifractality of quantum wave packets

Cited by in corpus (13)

• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Coexistence of ergodic and weakly ergodic states in finite-height Wannier-Stark ladders
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Fate of localization in coupled free chain and disordered chain
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Exact mobility edges in quasiperiodic network models with slowly varying potentials
• Many-body critical phase in a quasiperiodic chain and dynamical Widom lines in Fock space properties
• Quantum localization in incommensurate tight-binding chains
• Exact mobility edges in a slowly varying quasiperiodic ladder model