Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks

Abstract

We provide a framework for understanding the gapless Kitaev spin liquid (KSL) in the language of tensor network(TN). Without introducing Majorana fermion, most of the features of the KSL including the symmetries, gauge structure, criticality and vortex-freeness are explained in a compact TN representation. Our construction reveals a hidden string gas structure of the KSL. With only two variational parameters to adjust, we obtain an accurate KSL ansatz with the bond dimension D = 8 in a compact form, where the energy is about 0.007% higher than the exact one. In addition, the opening of gap and non-Abelian phase driven by a magnetic field are naturally understood in our construction.

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Topological Order and Conformal Quantum Critical Points
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Robust non-Abelian spin liquid and possible intermediate phase in antiferromagnetic Kitaev model with magnetic field
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• Kitaev Materials
• Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Topological order from quantum loops and nets
• Spin-one bilinear-biquadratic model on a star lattice
• Resonating Valence Bond States with Trimer Motifs

Cited by in corpus (26)

• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets
• Tensor network wavefunction of $S=1$ Kitaev spin liquids
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Majorana-mediated spin transport without spin polarization in Kitaev quantum spin liquids
• Identification of a Kitaev Quantum Spin Liquid by Magnetic Field Angle Dependence
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Density matrix renormalization group boosted by Gutzwiller projected wave functions
• Excitation spectrum of spin-1 Kitaev spin liquids
• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• Anisotropy as a diagnostic test for distinct tensor network wavefunctions of integer and half-integer spin Kitaev quantum spin liquids
• Generating function for projected entangled-pair states
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Determining non-Abelian topological order from infinite projected entangled pair states
• Differentiable programming tensor networks for Kitaev magnets
• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation
• Quantum phase transition between spin liquid and spin nematics in spin-1 Kitaev honeycomb model
• Mott Insulator-like Bose-Einstein Condensation in a Tight-Binding System of Interacting Bosons with a Flat Band
• Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model
• Variational Tensor Network Operator
• Gauge symmetry of excited states in projected entangled-pair state simulations
• Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Variational methods for characterizing matrix product operator symmetries
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers