Fractional corner charges in a 2D super-lattice Bose-Hubbard model

Abstract

We study a two dimensional super-lattice Bose-Hubbard model with alternating hoppings in the limit of strong on-site interactions. We evaluate the phase diagram of the model around half-filling using the density matrix renormalization group method and find two gapped phases separated by a gapless superfluid region. We demonstrate that the gapped states realize two distinct higher order symmetry protected topological phases, which are protected by a combination of charge conservation and $C_4$ lattice symmetry. The phases are distinguished in terms of a quantized fractional corner charge and a many-body topological invariant that is robust against arbitrary, symmetry preserving edge manipulations. We support our claims by numerically studying the full counting statistics of the corner charge, finding a sharp distribution peaked around the quantized values. These results are experimentally observable in ultracold atomic settings using state of the art quantum gas microscopy.

References in corpus (48)

• Many-Body Physics with Ultracold Gases
• Unpaired Majorana fermions in quantum wires
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Reflection symmetric second-order topological insulators and superconductors
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Classifying quantum phases using Matrix Product States and PEPS
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Tunable gauge potential for neutral and spinless particles in driven lattices
• The Zak phase and the existence of edge states in graphene
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Fragile Topology and Wannier Obstructions
• Microscopy of the interacting Harper-Hofstadter model in the few-body limit
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Topological phases protected by point group symmetry
• Gauging spatial symmetries and the classification of topological crystalline phases
• Topological edge states in the one-dimensional super-lattice Bose-Hubbard model
• Boundary Green functions of topological insulators and superconductors
• Topology of Disconnected Elementary Band Representations
• Quantized Berry Phases as Local Order Parameters of Quantum Liquids
• Perfect Sampling with Unitary Tensor Networks
• Generalized Inverse Participation Ratio as a Possible Measure of Localization for Interacting Systems
• Particle number fractionization of an atomic Fermi-Dirac gas in an optical lattice
• Fractional corner charges in spin-orbit coupled crystals
• Theory of interacting topological crystalline insulators
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Higher-order Topological Mott Insulators
• Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light
• Crystalline topological phases as defect networks
• Difficulties in operator-based formulation of the bulk quadrupole moment
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
• Fragile topological phases in interacting systems
• Higher Order Bosonic Topological Phases in Spin Models
• Interaction effects on the classification of crystalline topological insulators and superconductors

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• Thouless Pumps and Bulk-Boundary Correspondence in Higher-Order Symmetry-Protected Topological Phases
• Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
• High-order topological pumping on a superconducting quantum processor
• Growing Extended Laughlin States in a Quantum Gas Microscope: A Patchwork Construction
• Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Chiral orbital order of interacting bosons without higher bands
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Higher-order topological quantum paramagnets
• Deconfined Quantum Phase Transition of a Higher-Order Symmetry-Protected Topological State