Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method

Abstract

We report on recent results for strongly frustrated quantum $J_1$-$J_2$ antiferromagnets in dimensionality d=1,2,3 obtained by the coupled cluster method (CCM). We demonstrate that the CCM in high orders of approximation allows us to investigate quantum phase transitions driven by frustration and to discuss novel quantum ground states. In detail we consider the ground-state properties of (i) the Heisenberg spin-1/2 antiferromagnet on the cubic lattice in d=1,2,3, and use the results for the energy, the sublattice magnetization and the spin stiffness as a benchmark test for the precision of the method; (ii) coupled frustrated spin chains (the quasi-one-dimensional $J_1$--$J_2$ model) and discuss the influence of the quantum fluctuations and the interchain coupling on the incommensurate spiral state present in the classical model; (iii) the Shastry-Sutherland antiferromagnet on the square lattice; and (iv) a stacked frustrated square-lattice Heisenberg antiferromagnet (the quasi-two-dimensional $J_1$--$J_2$ model), and discuss the influence of the interlayer coupling on the quantum paramagnetic ground-state phase that is present for the strictly two-dimensional model.

16 pages, 7 figures, to appear in Proc. of "The 30th International Workshop on Condensed Matter theories" June 2006

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• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields
• Quantum s = 1/2 Antiferromagnets on Archimedean Lattices: The Route from Semiclassical Magnetic Order to Nonmagnetic Quantum States
• 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
• Cluster Density Matrix Embedding Theory for Quantum Spin Systems
• Ground-state properties of the triangular-lattice Heisenberg antiferromagnet with arbitrary spin quantum number $s$
• High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States
• 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
• The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB$m$ Approximation Scheme for Lattice Models
• Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: High-order coupled-cluster calculations
• Hidden magnetic order in CuNCN
• The Spin-Half {\it XXZ} Antiferromagnet on the Square Lattice Revisited: A High-Order Coupled Cluster Treatment
• Coupled Cluster Treatment of the Alternating Bond Diamond Chain