Transition to the Haldane phase driven by electron-electron correlations

Abstract

One of the most famous quantum systems with topological properties, the spin $\mathcal{S}=1$ antiferromagnetic Heisenberg chain, is well-known to display exotic $\mathcal{S}=1/2$ edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons -- the two-orbital Hubbard model -- with increasing repulsion strength $U$ and Hund interaction $J_{\mathrm{H}}$. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.

References in corpus (31)

• Colossal Magnetoresistant Materials: The Key Role of Phase Separation
• The density-matrix renormalization group
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Strong electronic correlations from Hund's coupling
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Dynamical density-matrix renormalization-group method
• Janus-faced influence of the Hund's rule coupling in strongly correlated materials
• Hidden order in 1D Bose insulators
• Density matrix renormalization group algorithms with a single center site
• Rise and fall of hidden string order of lattice bosons
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Phase Transitions Between Topologically Distinct Gapped Phases in Isotropic Spin Ladders
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• String order and adiabatic continuity of Haldane chains and band insulators
• Continuum in the spin excitation spectrum of a Haldane chain, observed by neutron scattering in CsNiCl3
• Edge states in Open Antiferromagnetic Heisenberg Chains
• Fragility of String Orders
• Structure of end states for a Haldane Spin Chain
• Topological quantum critical points in the extended Bose-Hubbard model
• The properties of Haldane excitations and multi-particle states in the antiferromagnetic spin-1 chain compound CsNiCl
• Fragility of Symmetry Protected Topological Order on a Hubbard Ladder
• Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet
• Finite-Temperature Dynamics and Thermal Intraband Magnon Scattering in Haldane Spin-One Chains
• Emergence of Superconductivity in Doped Multiorbital Hubbard Chains
• Magnetic excitations, non-classicality and quantum wake spin dynamics in the Hubbard chain
• Physics of integer spin antiferromagnetic chains : Haldane gaps and edge states
• Strongly anisotropic electronic and magnetic structures in oxide dichlorides RuOCl${}_2$ and OsOCl${}_2$
• Low-Lying Excitations in the S=1 Antiferromagnetic Heisenberg Chain
• Orbital-controlled magnetic transition between gapful and gapless phases in the Haldane system with t2g-orbital degeneracy

Cited by in corpus (7)

• Luther-Emery liquid and dominant singlet superconductivity in the hole-doped Haldane spin-1 chain
• Instability of the Haldane Phase: Roles of Charge Fluctuations and Hund's Coupling
• Topological Phase Transition in the Two-Leg Hubbard Model: Emergence of the Haldane Phase via Diagonal Hopping and Strong Interactions
• Two qubit gate with macroscopic singlet-triplet qubits in synthetic spin-one chains in InAsP quantum dot nanowires
• Evidence for valence-bond pairing in a one-dimensional two-orbital system
• Quasi-one-dimensional spin excitations in the iron pnictide NaFe${}_{0.53}$Cu${}_{0.47}$As
• Persistent Haldane Phase in Carbon Tetris Chains