Interacting second-order topological insulators in one-dimensional fermions with correlated hopping

Abstract

Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated hopping processes that break chiral invariance, but preserve both inversion and time-reversal symmetries. In this way, we show that our one-dimensional model gives rise to an interacting second-order topological insulating phase that supports gapped edge states. The topological nature of such interacting phase turns out to be revealed by both long-range order of a non-local string correlation function and by even degeneracy of the entanglement spectrum. For strong interactions we instead find that the topological crystalline phase is destroyed and replaced by a singlet superconducting phase. The latter, characterized by local fermionic pairing, turns out to appear both in a homogeneous and in a phase separated form. Relevantly, the derived one-dimensional model and the second-order topological insulator can be explored and investigated in atomic quantum simulators.

arXiv comment4 pages, 3 figures, updated Refs

References in corpus (114)

• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Real time evolution using the density matrix renormalization group
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Entanglement spectrum of a topological phase in one dimension
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Reflection symmetric second-order topological insulators and superconductors
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Observation of the supersolid stripe phase in spin-orbit coupled Bose-Einstein condensates
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Inversion Symmetric Topological Insulators
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Long-lived and transient supersolid behaviors in dipolar quantum gases
• Fragile Topology and Wannier Obstructions
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Floquet approach to ${\mathbb{Z}}_2$ lattice gauge theories with ultracold atoms in optical lattices
• Single particle Green's functions and interacting topological insulators
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Extended Bose-Hubbard Models with Ultracold Magnetic Atoms
• Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Microscopy of the interacting Harper-Hofstadter model in the few-body limit
• Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter
• Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• The low-energy Goldstone mode in a trapped dipolar supersolid
• Hidden order in 1D Bose insulators
• Higher Order Topological Phases: A General Principle of Construction
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Revealing Hidden Antiferromagnetic Correlations in Doped Hubbard Chains via String Correlators
• Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• Gapless topological phases and symmetry-enriched quantum criticality
• Topology and edge modes in quantum critical chains
• Geometric approach to fragile topology beyond symmetry indicators
• Topology of Disconnected Elementary Band Representations
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Photon-Assisted Tunneling in a Biased Strongly Correlated Bose Gas
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Eta-pairing states as true scars in an extended Hubbard Model
• Topological invariants and interacting one-dimensional fermionic systems
• Fragile topology and flat-band superconductivity in the strong-coupling regime
• Enhancement and sign change of magnetic correlations in a driven quantum many-body system
• Quantum localization bounds Trotter errors in digital quantum simulation
• Ground-state phase diagram of a spin-1/2 frustrated ferromagnetic XXZ chain: Haldane dimer phase and gapped/gapless chiral phases
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Strongly interacting Majorana modes in an array of Josephson junctions
• Characterization of a topological Mott insulator in one dimension
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Tunneling spectra simulation of interacting Majorana wires
• A Fermi-Hubbard Optical Tweezer Array
• Floquet dynamics in driven Fermi-Hubbard systems
• Symmetry-protected topological invariants of symmetry-protected topological phases of interacting bosons and fermions
• Symmetry-resolved entanglement in symmetry-protected topological phases
• Quantum scars of bosons with correlated hopping
• Exact Solution to Interacting Kitaev Chain at Symmetric Point
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• String order and adiabatic continuity of Haldane chains and band insulators
• Interaction effects on 1D fermionic symmetry protected topological phases
• Observation of Density-Induced Tunneling
• Symmetry-Breaking Topological Insulators in the ${\mathbb{Z}}_2$ Bose-Hubbard Model
• An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase
• Topological phases of a dimerized Fermi-Hubbard model for semiconductor nano-lattices
• Topological origin of edge states in two-dimensional inversion-symmetric insulators and semimetals
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Topological quantum critical points in the extended Bose-Hubbard model
• Quenched dynamics and spin-charge separation in an interacting topological lattice
• Symmetry protected topological phases of 1D interacting fermions with spin-charge separation
• Fragile topological phases in interacting systems
• How Hidden Orders Generate Gaps in 1D Fermionic Systems
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Excess charges as a probe of one-dimensional topological crystalline insulating phases
• Intertwined Topological Phases induced by Emergent Symmetry Protection
• Non-Abelian Bloch oscillations in higher-order topological insulators
• Homogeneous and inhomogeneous magnetic phases of constrained dipolar bosons
• Incommmensurability and unconventional superconductor to insulator transition in the Hubbard model with bond-charge interaction
• Entanglement Spectrum of Su-Schrieffer-Heeger-Hubbard Model
• Nontrivial Haldane phase of an atomic two-component Fermi gas trapped in a 1d optical lattice
• Topology invisible to eigenvalues in obstructed atomic insulators
• Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach
• Quantum phase diagram of the half filled Hubbard model with bond-charge interaction
• Bose-Hubbard physics in synthetic dimensions from interaction Trotterization
• Gauge Theories for the Thermal Hall Effect
• (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions
• Haldane Topological Orders in Motzkin Spin Chains
• Correlated Fragile Topology: a Parton Approach
• Non-Abelian Chern-Simons Theory from a Hubbard-like Model
• Interaction induced fractionalization and topological superconductivity in the polar molecules anisotropic $t-J$ model
• Topological Devil's staircase in atomic two-leg ladders
• Hidden Magnetism in Periodically Modulated One Dimensional Dipolar Fermions
• Homogeneous and domain wall topological Haldane conductors with dressed Rydberg atoms
• Nanoscale phase separation and superconductivity in the one-dimensional Hirsch model
• Gapping fragile topological bands by interactions
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Phase separation in fermionic systems with particle-hole asymmetry
• Hidden XY structure of the bond-charge Hubbard model
• Mott transition and magnetism in a fragile topological insulator

Cited by in corpus (9)

• Topological invariants based on generalized position operators and application to the interacting Rice-Mele model
• Stabilization of Hubbard-Thouless pumps through nonlocal fermionic repulsion
• Charge and spin gaps of the ionic Hubbard model with density-dependent hopping
• Jordan-Wigner transformation constructed for spinful fermions at S=1/2 spins in one dimension
• Topological Phase Transitions with Zero Indirect Band Gap
• Many-body tunneling in a double-well potential
• Nonstandard Hubbard model and electron pairing
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Signatures of the Correlated-Hopping Interaction in Non-Linear Transport through a Quantum Dot