Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model

Abstract

We investigate the fate of hardcore bosons in a Harper-Hofstadter model which was experimentally realized by Aidelsburger et al. [Nature Physics 11 , 162 (2015)] at half filling of the lowest band. We discuss the stability of an emergent fractional Chern insulator (FCI) state in a finite region of the phase diagram that is separated from a superfluid state by a first-order transition when tuning the band topology following the protocol used in the experiment. Since crossing a first-order transition is unfavorable for adiabatically preparing the FCI state, we extend the model to stabilize a featureless insulating state. The transition between this phase and the topological state proves to be continuous, providing a path in parameter space along which an FCI state could be adiabatically prepared. To further corroborate this statement, we perform time-dependent DMRG calculations which demonstrate that the FCI state may indeed be reached by adiabatically tuning a simple product state.

7 pages, 7 figures, published version

References in corpus (15)

• The density-matrix renormalization group in the age of matrix product states
• Photovoltaic Hall effect in graphene
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Nearly-flat bands with nontrivial topology
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Fractional quantum Hall effect in the absence of Landau levels
• Equilibrium states of generic quantum systems subject to periodic driving
• Time-evolving a matrix product state with long-ranged interactions
• Fractional Quantum Hall Effect in Optical Lattices
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Optical lattice quantum Hall effect
• Continuous Preparation of a Fractional Chern Insulator

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• Realization of a fractional quantum Hall state with ultracold atoms
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• Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• ${\mathbb{Z}}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Recent Developments in Fractional Chern Insulators
• Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge
• Growing Extended Laughlin States in a Quantum Gas Microscope: A Patchwork Construction
• Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases
• Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence
• Performance of the rigorous renormalization group for first order phase transitions and topological phases
• Phase transitions of bosonic fractional quantum Hall effect in topological flat bands
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Floquet Flux Attachment in Cold Atomic Systems
• Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Detecting Hidden Order in Fractional Chern Insulators
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit
• Chiral Gravitons on the Lattice
• Topology in the space-time scaling limit of quantum dynamics
• Chiral Edge Excitations of $\nu =1/2$ Fractional Chern Insulators in the Bosonic Hofstadter Model