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.

6 + 4 pages, 9 figures

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Fractional Quantum Hall Effect in Optical Lattices
• An Aharonov-Bohm interferometer for determining Bloch band topology
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• Non-Abelian Statistics in a Quantum Antiferromagnet
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• Quantum gas microscopy with spin, atom-number and multi-layer readout
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Continuous Preparation of a Fractional Chern Insulator
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Skyrmion Ground States of Rapidly Rotating Few-Fermion Systems

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• Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
• Bayesian Optimization for Robust State Preparation in Quantum Many-Body Systems
• Detecting Hidden Order in Fractional Chern Insulators
• Circular Dichroism on the Edge of Quantum Hall Systems: From Many-Body Chern Number to Anisotropy Measurements
• Interaction-induced chiral-transport inversion
• 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
• Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators