Tensor network wavefunction of $S=1$ Kitaev spin liquids

Abstract

Recently there has been a great interest in understanding quantum spin liquid phases with varying spin magnitude, partly due to possible material realizations. A number of recent numerical computations suggest that the ground state of the S=1 Kitaev model may be a quantum spin liquid in analogy to the renowned $S$=$1/2$ model. On the other hand, the nature of the ground state remains elusive since the $S$=$1$ model is not exactly solvable in contrast to the $S$=$1/2$ model. In this work, we construct a tensor network ground state wavefunction for the S=1 Kitaev model, which is explicitly written in terms of physical spin operators. We explain how this class of wavefunctions can be successfully used for variational computations and compare the outcomes to known results on finite size systems. We establish the existence of distinct topological sectors on torus by constructing the minimally entangled states in the degenerate ground state manifold and evaluating topological entanglement entropy. Our results suggest that the ground state of the S=1 Kitaev model is a gapped quantum spin liquid with Z2 gauge structure and Abelian quasiparticles.

References in corpus (36)

• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Orbital order and fluctuations in Mott insulators
• Excitations in the field-induced quantum spin liquid state of alpha-RuCl3
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Kitaev magnetism in honeycomb RuCl3 with intermediate spin-orbit coupling
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Spin-orbit excitation energies, anisotropic exchange, and magnetic phases of honeycomb RuCl3
• Crystal structure and magnetism in $\alpha$-RuCl3: an ab-initio study
• Anomalous thermal conductivity and magnetic torque response in the honeycomb magnet $\alpha$-RuCl${}_3$
• Emergence of a Field-Driven U(1) Spin Liquid in the Kitaev Honeycomb Model
• Spin-orbit excitations and electronic structure of the putative Kitaev magnet $\alpha$-RuCl${}_3$
• Microscopic mechanism for higher-spin Kitaev model
• Probing $\alpha$-RuCl${}_3$ Beyond Magnetic Order: Effects of Temperature and Magnetic Field
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Generalized Elitzur's Theorem and Dimensional Reduction
• Quantum spin liquid signatures in Kitaev-like frustrated magnets
• Finite field regime for a quantum spin liquid in $\alpha$-RuCl${}_3$
• Robust non-Abelian spin liquid and possible intermediate phase in antiferromagnetic Kitaev model with magnetic field
• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets
• One Proximate Kitaev Spin Liquid in the $K$-$J$-$\Gamma$ Model on the Honeycomb Lattice
• Electronic Structure of the Kitaev Material $\alpha$-${\text{RuCl}}_3$ Probed by Photoemission and Inverse Photoemission Spectroscopies
• Ground-state and thermodynamic properties of an $S=1$ Kitaev model
• ARPES study of the Kitaev Candidate $\alpha$-RuCl${}_3$
• Path to stable quantum spin liquids in spin-orbit coupled correlated materials
• Incipient and well-developed entropy plateaus in spin-S Kitaev models
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• Residual Entropy and Spin Fractionalizations in the Mixed-Spin Kitaev Model
• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation

Cited by in corpus (35)

• Quantum Machine Learning for Chemistry and Physics
• Static and dynamic magnetic properties of honeycomb lattice antiferromagnets Na${}_2{M}_2$TeO${}_6$, $M$ = Co and Ni
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Spin-1 Kitaev-Heisenberg model on a two-dimensional honeycomb lattice
• Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion
• Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids
• Characterizing spin-one Kitaev quantum spin liquids
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• Unusual excitations and double-peak specific heat in a bond-alternating spin-$1$ $K$-$\Gamma$ chain
• ${\mathbb{Z}}_2$ spin liquids in the higher spin-$S$ Kitaev honeycomb model: An exact deconfined ${\mathbb{Z}}_2$ gauge structure in a non-integrable model
• Excitation spectrum of spin-1 Kitaev spin liquids
• Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies
• Majorana correlations in the Kitaev model with ordered-flux structures
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Anisotropy as a diagnostic test for distinct tensor network wavefunctions of integer and half-integer spin Kitaev quantum spin liquids
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Field stability of Majorana spin liquids in antiferromagnetic Kitaev models
• Insights into the Anisotropic Spin-$S$ Kitaev Chain
• Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Phase diagrams of spin-$S$ Kitaev ladders
• Quantum many-body scars in spin-1 Kitaev chain with uniaxial single-ion anisotropy
• Quantum phase transition between spin liquid and spin nematics in spin-1 Kitaev honeycomb model
• Chiral spin state and nematic ferromagnet in the spin-1 Kitaev-$\Gamma$ model
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Dynamic structure factor of the antiferromagnetic Kitaev model in large magnetic fields
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Interplay of Kitaev Interaction and Off-diagonal Exchanges: Exotic Phases and Quantum Phase Diagrams
• Chiral bosonic quantum spin liquid in the integer-spin Heisenberg-Kitaev model
• Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks
• Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry
• Schwinger boson theory for $S=1$ Kitaev quantum spin liquids
• Sizable Ligand-Mediated Bond-Dependent Interactions in a Spin-1 Triangular Antiferromagnet NiI${}_2$