Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms

Abstract

We study the extent of the spin liquid phases in the Kitaev-Heisenberg model using infinite Projected Entangled-Pair States tensor network ansatz wave functions directly in the thermodynamic limit. To assess the accuracy of the ansatz wave functions we perform benchmarks against exact results for the Kitaev model and find very good agreement for various observables. In the case of the Kitaev-Heisenberg model we confirm the existence of 6 different phases: Néel, stripy, ferromagnetic, zigzag and two spin liquid phases. We find finite extents for both spin liquid phases and discontinuous phase transitions connecting them to symmetry-broken phases.

arXiv comment9 pages, 7 figures. Adjusted notation in equations 4-8. Added bond labeling to lower panel in figure 1. Included missing acknowledgements

References in corpus (35)

• Anyons in an exactly solved model and beyond
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Matrix product states represent ground states faithfully
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Criticality, the area law, and the computational power of PEPS
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Corner Transfer Matrix Renormalization Group Method
• Coarse-graining renormalization by higher-order singular value decomposition
• Experimental realization of a 2D fractional quantum spin liquid
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Tensor network study of the Shastry-Sutherland model in zero magnetic field
• Na2IrO3 as a molecular orbital crystal
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Magnetization of SrCu2(BO3)2 in ultrahigh magnetic fields up to 118 T
• Spin-orbital quantum liquid on the honeycomb lattice
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Unifying Projected Entangled Pair States contractions
• LevelScheme: A level scheme drawing and scientific figure preparation system for Mathematica
• Quantum Phase Transition in Heisenberg-Kitaev Model
• Tensor renormalization group study of classical XY model on the square lattice
• Global phase diagram of a doped Kitaev-Heisenberg model
• Competition between d-wave and topological p-wave superconductivity in the doped Kitaev-Heisenberg model

Cited by in corpus (46)

• Models and Materials for Generalized Kitaev Magnetism
• Variational optimization with infinite projected entangled-pair states
• Gradient methods for variational optimization of projected entangled-pair states
• Dynamics of the Kitaev-Heisenberg Model
• Heisenberg-Kitaev physics in magnetic fields
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Spin-1 Kitaev-Heisenberg model on a two-dimensional honeycomb lattice
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Heisenberg-Kitaev model in a magnetic field: $1/S$ expansion
• Field-induced quantum spin liquid in the Kitaev-Heisenberg model and its relation to $\alpha$-RuCl${}_3$
• Variational study of the Kitaev-Heisenberg-Gamma model
• Emergent Haldane phase in the $S=1$ bilinear-biquadratic Heisenberg model on the square lattice
• Magnetic Field Induced Spin Liquids in S=1 Kitaev Honeycomb Model
• Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
• A universal tensor network algorithm for any infinite lattice
• Field-enhanced quantum fuctuation in S=1/2 frustrated square lattice
• Infinite Projected Entangled-Pair State algorithm for ruby and triangle-honeycomb lattices
• A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids
• Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• Tensor network simulation of the Kitaev-Heisenberg model at finite temperature
• Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice
• Comprehensive study of the global phase diagram in the triangular $J$-$K$-$\Gamma$ model
• Ground state properties of $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$ determined from $\text{ab initio}$ Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions
• Quantum Monte Carlo Simulation of Generalized Kitaev Models
• Fermionic approach to variational quantum simulation of Kitaev spin models
• Spin-$S$ Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Phonon Dynamics in the Generalized Kitaev Spin Liquid
• Differentiable programming tensor networks for Kitaev magnets
• A continuum of compass spin models on the honeycomb lattice
• Single-hole spectra of Kitaev spin liquids: from dynamical Nagaoka ferromagnetism to spin-hole fractionalization
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study
• Majorana Fermion Mean-Field Theories of Kitaev Quantum Spin Liquids
• Magnetic order and spin excitations in the Kitaev--Heisenberg model on the honeycomb lattice
• Phase diagram of the Kitaev-Heisenberg model using various finite-size clusters
• Inferring Hidden Symmetries of Exotic Magnets from Detecting Explicit Order Parameters
• Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Topological phases of the compass ladder model
• Magnetic excitations in the Kitaev material Na${}_2$IrO${}_3$ studied by neutron scattering
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers