Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points

Abstract

We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS.

13 pages; 19 figures

References in corpus (56)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• 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
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Quantum critical phase with infinite projected entangled paired states
• Direct Calculation of the Spin Stiffness in the $J_1$--$J_2$ Heisenberg Antiferromagnet
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• Spin liquid phase for the frustrated Quantum Heisenberg Antiferromagnet on a square lattice
• Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry
• Generic mixed columnar-plaquette phases in Rokhsar-Kivelson models
• Gradient optimization of finite projected entangled pair states
• Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
• Plaquette valence-bond solid in the square lattice J1-J2 antiferromagnet Heisenberg model: a bond operator approach
• Low temperature broken symmetry phases of spiral antiferromagnets
• Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model
• Phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice
• Master equation approach to computing RVB bond amplitudes
• Accurate simulation for finite projected entangled pair states in two dimensions
• A Generalized Quantum Dimer Model Applied to the Frustrated Heisenberg Model on the Square Lattice: Emergence of a Mixed Columnar-Plaquette Phase
• Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet
• Valence bond spin liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets
• Numerical evidence for the spin-Peierls state in the frustrated quantum antiferromagnet
• Plaquette Order in the J1-J2-J3 model: a series expansion analysis
• Continuous phase transition from Néel state to Z_2 spin liquid state on a square lattice
• Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states
• Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid
• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• Phase diagram and magnetic excitations of $J_1$-$J_3$ Heisenberg model on the square lattice

Cited by in corpus (10)

• Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
• Foundation Neural-Networks Quantum States as a Unified Ansatz for Multiple Hamiltonians
• Engineering frustrated Rydberg spin models by graphical Floquet modulation
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• Fractionalized Fermi liquids and the cuprate phase diagram
• Single-layer framework of variational tensor network states
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• Vestigial Nematic Order at Zero Temperature in Two-Dimensional Frustrated Quantum Antiferromagnets
• Grassmann tensor networks
• Frustration-induced degenerate spin state with up-up-down-down ordering in corner-connected Heisenberg square-plaquettes