Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry

Abstract

A novel nonlinear sigma model method is proposed for the two-dimensional J1-J2 model, which is extended to include plaquette-type distortion. The nonlinear sigma model is properly derived without spoiling the original spin degrees of freedom. The method shows that a single disordered phase continuously extends from a frustrated uniform regime to an unfrustrated distorted regime. By the continuity and Oshikawa's commensurability condition, the disordered ground states for the uniform J1-J2 model are plaquette states with four-fold degeneracy.

4 pages (including 2 figures)

References in corpus (19)

• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Green Function Monte Carlo with Stochastic Reconfiguration
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Li${}_2$VO(Si,Ge)O${}_4$, a prototype of a two-dimensional frustrated quantum Heisenberg antiferromagnet
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• New quantum phase transitions in the two-dimensional J1-J2 model
• New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
• Magnetic and thermodynamic properties of Li(2)VOSiO(4): a two-dimensional S=1/2 frustrated antiferromagnet on a square lattice
• Realization of a large J_2 quasi-2D spin-half Heisenberg system: Li2VOSiO4
• Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensional J1-J2 model
• Very low-frequency excitations in frustrated two-dimensional $S=1/2$ Heisenberg antiferromagnets
• Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model
• Non-Linear Sigma Model for Inhomogeneous Spin Chains
• Phase Diagrams of Mixed Spin Chains with Period 4 by the Nonlinear $\sigma$ Model
• Two-Dimensional Quantum Spin Systems with Ladder and Plaquette Structure
• Quantum Phase Transitions in Two-Dimensional Spin Systems with Ladder, Plaquette and Mixed-Spin Structures
• Quantum disorder due to singlet formation: The Plaquette lattice

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• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu${}_2$(BO${}_3$)${}_2$
• Spin-gap phase of a quantum spin system on a honeycomb lattice
• Plaquette valence-bond solid in the square lattice J1-J2 antiferromagnet Heisenberg model: a bond operator approach
• Randomness-induced quantum spin liquid behavior in the $s=\frac{1}{2}$ random $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice
• Randomness-induced quantum spin liquid behavior in the s=1/2 random J1-J2 Heisenberg antiferromagnet on the honeycomb lattice
• Master equation approach to computing RVB bond amplitudes
• Spectral properties of the square-lattice antiferromagnetic J1-J2 Heisenberg model: confinement and deconfinement of spinons
• Cluster Density Matrix Embedding Theory for Quantum Spin Systems
• Spin liquid versus dimer phases in an anisotropic J1-J2 frustrated square antiferromagnet
• Block product density matrix embedding theory for strongly correlated spin systems
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• The Ising phase in the J1-J2 Heisenberg Model
• The Phase Transition of Square Lattice Antiferromagnets at Finite Temperature
• Spin excitation spectra of the two dimensional $S=1/2$ Heisenberg model with a checkerboard structure
• Anomalous Spin Dynamics observed by High Frequency ESR in Honeycomb Lattice Antiferromagnet InCu2/3V1/3O3
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Chern-Simons superconductors and their instabilities
• 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
• Symmetry-projected cluster mean-field theory applied to spin systems
• Magnetic quantum phase transitions of the antiferromagnetic J_{1}-J_{2} Heisenberg model
• Entanglement in first excited states of some many-body quantum spin systems: indication of quantum phase transition in finite size systems
• Regge Trajectories of Exotic Hadrons in the Flux Tube Model
• Phase Diagram of the Frustrated Square-Lattice Hubbard Model: Variational Cluster Approach
• Linear combinations of cluster mean-field states applied to spin systems
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• 2D excitation information by MPS method on infinite helixes
• Thermal Hall conductivity of a valence bond solid phase in the square lattice $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction
• Deconfinement phase transition in a two-dimensional model of interacting $2\times 2$ plaquettes
• Bound state of a hole and a triplet spin in the $t_1$-$t_2$-$J_1$-$J_2$ model
• The quantum J_{1}-J_{1'}-J_{2} spin-1/2 Heisenberg antiferromagnet: A variational method study
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states