Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model

Abstract

Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor $\nu =1$ and find strong indications that at $\alpha =1/6$ magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at $\nu =1$, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.

arXiv comment6 + 4 pages, 9 figures

References in corpus (48)

• The density-matrix renormalization group in the age of matrix product states
• Experimental realisation of the topological Haldane model
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional quantum Hall states of atoms in optical Lattices
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• Rapidly Rotating Bose-Einstein Condensates in and near the Lowest Landau Level
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Is the Composite Fermion a Dirac Particle?
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Microscopy of the interacting Harper-Hofstadter model in the few-body limit
• Fractional Quantum Hall Effect in Optical Lattices
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Artificial gauge fields in materials and engineered systems
• Quantum Hall fractions in rotating Bose-Einstein condensates
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect
• A Composite Fermion Description of Rotating Bose-Einstein Condensates
• Observation of Four-body Ring-exchange Interactions and Anyonic Fractional Statistics
• Non-Abelian Quantum Hall Effect in Topological Flat Bands
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• Spin-resolved single-atom imaging of ${}^6$Li in free space
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Probing Non-Abelian Statistics with QuasiParticle Interferometry
• Interferometric Measurements of Many-body Topological Invariants using Mobile Impurities
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• Cooper Instability of Composite Fermions
• Realizing and Adiabatically Preparing Bosonic Integer and Fractional Quantum Hall states in Optical Lattices
• Quantum Hall fractions for spinless Bosons
• Parent Hamiltonian for the non-Abelian chiral spin liquid
• Adiabatic Path to Fractional Quantum Hall States of a Few Bosonic Atoms
• Quantum gas microscopy with spin, atom-number and multi-layer readout
• Detecting fractional Chern insulators through circular dichroism
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Continuous Preparation of a Fractional Chern Insulator
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement
• Probing the Hall Voltage in Synthetic Quantum Systems
• Skyrmion Ground States of Rapidly Rotating Few-Fermion Systems
• PH-Pfaffian order in a translationally and rotationally invariant system

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• Chiral Gravitons on the Lattice
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code
• Absence of gapless Majorana edge modes in few-leg bosonic flux ladders
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states