Characterizing fractional topological phases of lattice bosons near the first Mott lobe

2021/11/30 by Julian Boesl, Rohit Dilip, Frank Pollmann +1
Physics and Astronomy · #Boson #Condensed matter physics #Density matrix renormalization group #Fractional quantum Hall effect #Magnetic field #Mott insulator #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum spin Hall effect #Renormalization group #Topological insulator #Topological order #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.quant-gas #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.105.075135

published as Phys. Rev. B 105, 075135 (2022) · 8 pages, 6 figures, published version

openalex created_date 2021/12/06 · openalex publication_date 2022/02/18 · arxiv created 2022/02/21 · arxiv updated 2022/02/23 · openalex updated_date 2026/08/06

Abstract

The Bose-Hubbard model subjected to an effective magnetic field hosts a plethora of phases with different topological orders when tuning the chemical potential. Using the density matrix renormalization group method, we identify several gapped phases near the first Mott lobe at strong interactions. They are connected by a particle-hole symmetry to a variety of quantum Hall states stabilized at low fillings. We characterize phases of both particle and hole type and identify signatures compatible with Laughlin, Moore-Read, and bosonic integer quantum Hall states by calculating the quantized Hall conductance and by extracting the topological entanglement entropy. Furthermore, we analyze the entanglement spectrum of Laughlin states of bosonic particles and holes for a range of interaction strengths, as well as the entanglement spectrum of a Moore-Read state. These results further corroborate the existence of topological states at high fillings, close to the first Mott lobe, as hole analogs of the respective low-filling states.

Citations

• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
• Bosonic Integer Quantum Hall Effect in an Interacting Lattice Model
• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Phase boundary of the boson Mott insulator in a rotating optical lattice
• Two-Dimensional Magnetotransport in the Extreme Quantum Limit
• Detecting Topological Order in a Ground State Wave Function
• Quantum Hall Fractions in Rotating Bose-Einstein Condensates
• Single-site-resolved measurement of the current statistics in optical lattices
• Characterizing Topological Order by Studying the Ground States on an Infinite Cylinder
• Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices
• Flux insertion, entanglement, and quantized responses
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• Fractional Quantum Hall States of Atoms in Optical Lattices
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Edge-mode combinations in the entanglement spectra of non-Abelian fractional quantum Hall states on the torus
• Nonabelions in the fractional quantum hall effect
• Anyonic interferometry and protected memories in atomic spin lattices
• Characterization and stability of a fermionicν=1/3fractional Chern insulator
• Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Interaction-driven plateau transition between integer and fractional Chern Insulators