High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

Abstract

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. Néel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half $J_1$--$J_2$ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at $J_2/J_1=0.5$. The dimerized phase is stable over a range of values for $J_2/J_1$ around 0.5. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of $J_2/J_1$. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the Néel and the dimerized phases. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV${}_4$O${}_9$ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, Néel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits.

34 pages, 13 figures, 2 tables

References in corpus (46)

• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Exact dimer ground state of the two dimensional Heisenberg spin system SrCu_2(BO_3)_2
• Quantum Phase Transitions in the Shastry-Sutherland Model for $\mathbf{SrC}{\mathbf{u}}_2(\mathbf{B}{\mathbf{O}}_3{)}_2$
• DMRG Studies of the Spin-Half Heisenberg System with Dimerization and Frustration
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Phase diagram of depleted Heisenberg model for CaV4O9
• Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Plaquette Resonating-Valence-Bond Ground State of CaV${}_4$O${}_9$
• An efficient implementation of high-order coupled-cluster techniques applied to quantum magnets
• Exact Demonstration of Magnetization Pleateaus and First Order Dimer-Néel Phase Transitions in a Modified Shastry-Sutherland Model for SrCu${}_2$(BO${}_3$)${}_2$
• Phase Diagram of the quadrumerized Shastry-Sutherland Model
• Various series expansions for a Heisenberg antiferromagnet model for SrCu${}_2$(BO${}_3$)${}_2$
• Quantum Phases of the Shastry-Sutherland Antiferromagnet
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• First order transition between magnetic order and valence-bond order in a 2D frustrated Heisenberg model
• Phase Transitions in the Spin-Half J_1--J_2 Model
• Quantum Phase Transitions of a Square-Lattice Heisenberg Antiferromagnet with Two Kinds of Nearest-Neighbour Bonds: A High-Order Coupled-Cluster Treatment
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• High-Order Coupled Cluster Method Calculations for the Ground- and Excited-State Properties of the Spin-Half XXZ Model
• Critical exponents of the quantum phase transition in a planar antiferromagnet
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin-$\frac{1}{2}$ $XXZ$ Models
• The quantum $J_1$--$J_1^{\prime }$--$J_2$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• A numerical method for detecting incommensurate correlations in the Heisenberg zigzag ladder
• Coupled Cluster Treatment Of An Interpolating Triangle/Kagome Antiferromagnet
• Detecting spontaneous symmetry breaking in finite-size spectra of frustrated quantum antiferromagnets
• Convergent expansions for properties of the Heisenberg model for CaV${}_4$O${}_9$
• Coupled Cluster Method Calculations Of Quantum Magnets With Spins Of General Spin Quantum Number
• Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method
• A microscopic approach to the dimerization in the frustrated spin-1/2 antiferromagnetic chains
• Magnetic phases of the mixed-spin $J_1-J_2$ Heisenberg model on a square lattice
• The quantum $J_1$-$J_1^{\prime }$-$J_2$ spin-1/2 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor regular bonds
• Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• High-Order Coupled Cluster Calculations Via Parallel Processing: An Illustration For CaV${}_4$O${}_9$
• Influence of quantum fluctuations on zero-temperature phase transitions between collinear and noncollinear states in frustrated spin systems
• Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method
• Coupled Cluster Treatment of the XY model
• Quantum phase transitions in the J-J' Heisenberg and XY spin-1/2 antiferromagnets on square lattice: Finite-size scaling analysis
• Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: High-order coupled-cluster calculations
• The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets
• Ab Initio Treatments of the Ising Model in a Transverse Field
• Influence of the spin quantum number $s$ on the zero-temperature phase transition in the square lattice $J$-$J^{\prime }$ model
• Two-dimensional S=1/2 antiferromagnet on a plaquette lattice

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• Quasiclassical magnetic order and its loss in a spin-1/2 Heisenberg antiferromagnet on a triangular lattice with competing bonds
• High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: $J_1$--$J_2$ model
• The frustrated Heisenberg antiferromagnet on the checkerboard lattice: the $J_1$--$J_2$ model
• Magnetic order on a frustrated spin-1/2 Heisenberg antiferromagnet on the Union Jack lattice
• Ground-state phases of the frustrated spin-1/2 $J_1$--$J_2$--$J_3$ Heisenberg ferromagnet ($J_1<0$) on the honeycomb lattice with $J_3=J_2>0$
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• Coupled cluster and perturbation theories based on a cluster mean-field reference applied to strongly correlated spin systems
• A frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model
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• Analytical and numerical studies of the one-dimensional sawtooth chain
• Magnetic order in spin-1 and spin-3/2 interpolating square-triangle Heisenberg antiferromagnets
• Ground-state phase diagram of the spin-1/2 square-lattice J1-J2 model with plaquette structure
• A frustrated quantum spin-${\boldmath s}$ model on the Union Jack lattice with spins ${\boldmath s>1/2}$
• Symmetry-projected cluster mean-field theory applied to spin systems
• Projective symmetry group classification of Abrikosov fermion mean-field ansätze on the square-octagon lattice
• Non-Coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method
• Frustration induced noncollinear magnetic order phase in one-dimensional Heisenberg chain with alternating antiferromagnetic and ferromagnetic next nearest neighbor interactions
• Linear combinations of cluster mean-field states applied to spin systems
• Coupled Cluster Treatment of the Alternating Bond Diamond Chain
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model