Stark localization near Aubry-André criticality

Abstract

In this work, we investigate the Stark localization near the Aubry-André (AA) critical point. We perform careful studies for reporting system-dependent parameters, such as localization length, inverse participation ratio (IPR), and energy gap between the ground and first excited state, for characterizing the localization-delocalization transition. We show that the scaling exponents possessed by these key descriptors of localization are quite different from that of a pure AA model or Stark model. Near the critical point of the AA model, in the presence of Stark field of strength $h$, the localization length $\zeta$ scales as $\zeta \propto h^{-\nu }$ with $\nu \approx 0.29$ which is different than both the pure AA model ($\nu =1$) and Stark model ($\nu \approx 0.33$). The IPR in this case scales as IPR $\propto h^s$ with $s\approx 0.096$ which is again significantly different than both the pure AA model ($s\approx 0.33$) and Stark model ($s\approx 0.33$). The energy gap, $\Delta$, scales as $E\propto h^{\nu z}$, where $z\approx 2.37$ which is however same as the pure AA model. Finally, we discuss how invoking a criticality inducing additional control parameter may help in designing better many-body quantum sensors. Quantum critical sensors exploit the venerability of the wavefunction near the quantum critical point against small parameter shifts. By incorporating a control parameter in the form of the quasi-periodic field, i.e., the AA potential, we show a significant advantage can be drawn in estimating an unknown parameter, which is considered here to be the Stark weak field strength, with high precision.

arXiv comment8 pages, 6 figures

References in corpus (66)

• Quantum metrology
• Many body localization and thermalization in quantum statistical mechanics
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Anderson Transitions
• Many-body localization, thermalization, and entanglement
• Anderson localization of a non-interacting Bose-Einstein condensate
• Topological energy transfer in an optomechanical system with exceptional points
• Visualization of Branch Points in PT-Symmetric Waveguides
• Super-resolving phase measurements with a multi-photon entangled state
• Beating the Standard Quantum Limit with Four Entangled Photons
• Quantum Annealing and Analog Quantum Computation
• Defects in correlated metals and superconductors
• Strongly Correlated Quantum Walks in Optical Lattices
• Quantum noise limited and entanglement-assisted magnetometry
• Many-Body Localization in a Quasiperiodic System
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• 'Designer atoms' for quantum metrology
• Quantum criticality as a resource for quantum estimation
• Magnetic sensitivity beyond the projection noise limit by spin squeezing
• Influence of Generic Scale Invariance on Classical and Quantum Phase Transitions
• Stark many-body localization
• From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
• Detection of quantum critical points by a probe qubit
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Direct observation of quantum criticality in Ising spin chains
• Anomalous transport in the Aubry-André-Harper model in isolated and open systems
• Quantum transport and localization in 1d and 2d tight-binding lattices
• Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases
• Anderson localization of electromagnetic waves in three dimensions
• Stark many-body localization: Evidence for Hilbert-space shattering
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Kibble-Zurek mechanism with a single particle: dynamics of the localization-delocalization transition in the Aubry-André model
• Delocalization of weakly interacting bosons in a 1D quasiperiodic potential
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Critical Exponents of the Superfluid-Bose Glass Transition in Three-Dimensions
• Many-body localization in tilted and harmonic potentials
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Wannier-Stark states and Bloch oscillations in the honeycomb lattice
• Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems
• Bose glass transition and spin-wave localization for 2D bosons in a random potential
• Spectral function and fidelity susceptibility in quantum critical phenomena
• Mobility edge of Stark many-body localization
• Many-body dynamical phase transition in quasi-periodic potential
• Stark localization as a resource for weak-field sensing with super-Heisenberg precision
• Localization Driven Quantum Sensing
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Enhancement of Quantum Correlation Length in Quenched Disordered Spin Chains
• Quantum criticality in the disordered Aubry-André model
• Classical Spin Models with Broken Continuous Symmetry: Random Field Induced Order and Persistence of Spontaneous Magnetization
• Beating no-go theorems by engineering defects in quantum spin models
• Classical spin models with broken symmetry: Random Field Induced Order and Persistence of spontaneous magnetization in presence of a random field
• Designing Robust Quantum Refrigerators in Disordered Spin Models
• Constructive Interference Between Disordered Couplings Enhances Multiparty Entanglement in Quantum Heisenberg Spin Glass Models
• Spontaneous magnetization of quantum $XY$ spin model in joint presence of quenched and annealed disorder
• Order-from-disorder and critical scalings of spontaneous magnetization in random-field quantum spin systems
• Multiple mobility edges in a 1D Aubry chain with Hubbard interaction in presence of electric field: Controlled electron transport
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Estimating phase transition of perturbed J1-J2 Heisenberg quantum chain in mixtures of ground and first excited states
• Trends of information backflow in disordered spin chains

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