Quantum Spin Liquids in Weak Mott Insulators with a Spin-Orbit Coupling

Abstract

The weak Mott insulating regime of the triangular lattice Hubbard model exhibits a rich magnetic phase diagram as a result of the ring exchange interaction in the spin Hamiltonian. These phases include the Kalmeyer-Laughlin type chiral spin liquid (CSL) and a valence bond solid (VBS). A natural question arises regarding the robustness of these phases in the presence of a weak spin-orbit coupling (SOC). In this study, we derive the effective spin model for the spin-orbit coupled triangular lattice Hubbard model in the weak Mott insulting regime, including all SOC-mediated spin-bilinears and ring-exchange interactions. We then construct a simplified spin model keeping only the most relevant SOC-mediated spin interactions. Using infinite density matrix renormalization group (iDMRG) we show that the CSL and VBS phases of the triangular lattice Hubbard model can be stabilized in the presence of a weak SOC. The stabilization results from a compensation between the Dzyaloshinskii-Moriya interaction and a SOC-mediated ring exchange interaction. We also provide additional qualitative arguments to intuitively understand the compensation mechanism in the iDMRG quantum phase diagrams. This mechanism for stabilization can potentially be useful for the experimental realization of quantum spin liquids.

20 pages, 14 figures

References in corpus (53)

• Anyons in an exactly solved model and beyond
• The density-matrix renormalization group
• Quantum Spin Liquids
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum Spin Liquid States
• Correlated quantum phenomena in the strong spin-orbit regime
• Quantum Spin Liquids
• Quantum Orders and Symmetric Spin Liquids
• Zoo of quantum-topological phases of matter
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Kitaev quantum spin liquid - concept and materialization
• A Field Guide to Spin Liquids
• The iTEBD algorithm beyond unitary evolution
• Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Topological and magnetic phases of interacting electrons in the pyrochlore iridates
• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Critical fermi surfaces and non-fermi liquid metals
• Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators
• Theory of a continuous Mott transition in two dimensions
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Kitaev Spin Liquid in 3d Transition Metal Compounds
• Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
• Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
• Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model
• Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip
• Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS${}_2$
• Weak Mott insulators on the triangular lattice: possibility of a gapless nematic quantum spin liquid
• Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice
• Mott transition between a spin-liquid insulator and a metal in three dimensions
• Ground state phase diagram of the triangular lattice Hubbard model by density matrix renormalization group method
• Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
• Novel Pauli-paramagnetic quantum phase in a Mott insulator
• Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder
• Geometrical frustration versus Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$
• Spin-liquid versus spiral-order phases in the anisotropic triangular lattice
• XY magnetism, Kitaev exchange, and long-range frustration in the $J_{\mathrm{eff}}=1/2$ honeycomb cobaltates
• Doped Mott Insulators in the Triangular Lattice Hubbard Model
• Frustrated magnetic interactions in a Wigner-Mott insulator
• Phase diagram of the anisotropic triangular lattice Hubbard model
• Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
• Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model
• Non-Kitaev vs. Kitaev Honeycomb Cobaltates
• A DMRG Study of Superconductivity in the Triangular Lattice Hubbard Model
• A continuous Mott transition between a metal and a quantum spin liquid
• Chiral Pseudo Spin Liquids in Moire Heterostructures
• Proximate Dirac spin liquid in honeycomb lattice $J_1$-$J_3$ XXZ model: Numerical study and application to cobaltates
• Dimensional decoupling at continuous quantum critical Mott transitions
• Electromagnetic signatures of chiral quantum spin liquid
• Frustrated Antiferromagnetic Triangular Lattice with Dzyaloshinskii-Moriya Interaction: Ground States, Spin Waves, Skyrmion Crystal, Phase Transition
• Signatures of spin-triplet excitations in optical conductivity of valence bond solids
• Electric field control of a quantum spin liquid in weak Mott insulators

Cited by in corpus (2)

• Exact diagonalization study of triangular Heisenberg model with four-spin ring-exchange interaction
• Effective spin model with anisotropic exchange interactions for the spin-orbit coupled Hubbard model at half-filling