arXiv subjects

D. J. J. Farnell

Publications and source records attributed to D. J. J. Farnell.

42 records · Page 3Linked to original sources

arXiv2000

Coupled Cluster Treatment Of An Interpolating Triangle/Kagome Antiferromagnet

The coupled cluster method (CCM) is applied to a spin-half model at zero temperature which interpolates between a triangular lattice antiferromagnet (TAF) and a Kagome lattice antiferromagnet (KAF). The strength of the bonds which connect Kagome lattice sites is J, and the strength of the bonds which link the non-Kagome lattice sites to the Kagome lattice sites on an underlying triangular lattice is J'. Our results are found to be highly converged, and our best estimate for the ground-state energy per spin for the spin-half KAF (J'=0) of -0.4252 constitutes one of the most accurate results yet found for this model. The amount of classical ordering on the Kagome lattice sites is also considered, and it is seen that this parameter goes to zero for values of J' very close the KAF point. Further evidence is also presented for CCM critical points which reinforce the conjecture that there is a phase near to the KAF point which is much different to that near to the TAF point (J=J').

cond-mat.supr-con↗

arXiv1999

Sign Rules for Anisotropic Quantum Spin Systems

We present new and exact ``sign rules'' for various spin-s anisotropic spin-lattice models. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive-definite. Using these results exact statements for various expectation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the effects of sign rules in variational calculations and quantum Monte Carlo calculations are considered. They are illustrated by a simple variational treatment of a one-dimensional anisotropic spin model.

cond-mat.str-el↗

arXiv1998

Ab Initio Simulation of the Nodal Surfaces of Heisenberg Antiferromagnets

The spin-half Heisenberg antiferromagnet (HAF) on the square and triangular lattices is studied using the coupled cluster method (CCM) technique of quantum many-body theory. The phase relations between different expansion coefficients of the ground-state wave function in an Ising basis for the square lattice HAF is exactly known via the Marshall-Peierls sign rule, although no equivalent sign rule has yet been obtained for the triangular lattice HAF. Here the CCM is used to give accurate estimates for the Ising-expansion coefficients for these systems, and CCM results are noted to be fully consistent with the Marshall-Peierls sign rule for the square lattice case. For the triangular lattice HAF, a heuristic rule is presented which fits our CCM results for the Ising-expansion coefficients of states which correspond to two-body excitations with respect to the reference state. It is also seen that Ising-expansion coefficients which describe localised, $m$-body excitations with respect to the reference state are found to be highly converged, and from this result we infer that the nodal surface of the triangular lattice HAF is being accurately modeled. Using these results, we are able to make suggestions regarding possible extensions of existing quantum Monte Carlo simulations for the triangular lattice HAF.

cond-mat.str-el↗

arXiv1997

Coupled Cluster Treatment of the XY model

We study quantum spin systems in the 1D, 2D square and 3D cubic lattices with nearest-neighbour XY exchange. We use the coupled-cluster method (CCM) to calculate the ground-state energy, the T=0 sublattice magnetisation and the excited state energies, all as functions of the anisotropy parameter $γ$. We consider $S=1/2$ in detail and give some results for higher $S$. In 1D these results are compared with the exact $S=1/2$ results and in 2D with Monte-Carlo and series expansions. We obtain critical points close to the expected value $γ=0$ and our extrapolated LSUBn results for the ground-state energy are well converged for all $γ$ except very close to the critical point.

cond-mat↗

arXiv1996

An efficient implementation of high-order coupled-cluster techniques applied to quantum magnets

We illustrate how the systematic inclusion of multi-spin correlations of the quantum spin-lattice systems can be efficiently implemented within the framework of the coupled-cluster method by examining the ground-state properties of both the square-lattice and the frustrated triangular-lattice quantum antiferromagnets. Various physical quantities including the ground-state energy, the anisotropy susceptibility, and the sublattice magnetisation are calculated and compared with those obtained from such other methods as series expansions and quantum Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv1995

Numerical and approximate analytical results for the frustrated spin-1/2 quantum spin chain

We study the $T=0$ frustrated phase of the $1D$ quantum spin-$\frac 12$ system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalisation group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.

cond-mat↗