Hubbard model for spin-1 Haldane chains

Abstract

The Haldane phase for antiferromagnetic spin-1 chains is a celebrated topological state of matter, featuring gapped excitations and fractional spin-1/2 edge states. Here, we provide numerical evidence that this phase can be realized with a Hubbard model at half filling, where each $s=1$ spin is stored in a four-site fermionic structure. We find that the noninteracting limit of our proposed model describes a one-dimensional topological insulator, and we conjecture it to be adiabatically connected to the Haldane phase. Our work suggests a route to build spin-1 networks using Hubbard model quantum simulators.

arXiv commentRevised version, including Supplemental Material

References in corpus (27)

• Entanglement spectrum of a topological phase in one dimension
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Magnetism in graphene nano-islands
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• The Zak phase and the existence of edge states in graphene
• The Hubbard Model
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Quantum simulation of a Fermi-Hubbard model using a semiconductor quantum dot array
• Detection of Symmetry Protected Topological Phases in 1D
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Observation of fractional edge excitations in nanographene spin chains
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
• Collective All-Carbon Magnetism in Triangulene Dimers
• Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain
• Engineering the eigenstates of coupled spin-1/2 atoms on a surface
• Exchange rules for diradical π-conjugated hydrocarbons
• Quantum Simulation of the Hubbard Model with Dopant Atoms in Silicon
• String order and adiabatic continuity of Haldane chains and band insulators
• Particle-Hole Symmetries in Condensed Matter
• The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
• Fragility of Symmetry Protected Topological Order on a Hubbard Ladder
• Local probe of fractional edge states of S=1 Heisenberg spin chains
• Probing local moments in nanographenes with electron tunneling spectroscopy
• Topological Kondo insulators in one dimension: Continuous Haldane-type ground-state evolution from the strongly-interacting to the non-interacting limit
• Designer fermion models in functionalized graphene bilayers

Cited by in corpus (12)

• Theory of intermolecular exchange in coupled spin-1/2 nanographenes
• Theory of triangulene two-dimensional crystals
• Pair-density-wave superconductor from doping Haldane chain and rung-singlet ladder
• Broken-symmetry magnetic phases in two-dimensional triangulene crystals
• Superexchange Mechanism in Coupled Triangulenes Forming Spin-1 Chains
• Multi-frequency control and measurement of a spin-7/2 system encoded in a transmon qudit
• Magnetic frustration and fractionalization in oligo(indenoindenes)
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• Two qubit gate with macroscopic singlet-triplet qubits in synthetic spin-one chains in InAsP quantum dot nanowires
• Persistent Haldane Phase in Carbon Tetris Chains
• Identification and optimization of accurate spin models for Fermi-Hubbard ladders using matrix product states
• Negative exchange interaction in Si quantum dot arrays via valley-phase induced ${\mathbb{Z}}_2$ gauge field