Search

We use the coupled cluster method implemented at high orders of approximation to study the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ model on the triangular lattice with Heisenberg interactions between nearest-neighbour and next-nearest-neighbour pairs of spins, with coupling strengths $J_{1}>0$ and $J_{2} \equiv \kappa J_{1} >0$, respectively. In the window $0 \leq \kappa \leq 1$ we find that the 3-sublattice 120$^{\circ}$ N\'{e}el-ordered and 2-sublattice 180$^{\circ}$ stripe-ordered antiferromagnetic states form the stable ground-state phases in the regions $\kappa \kappa^{c}_{2} = 0.165(5)$, respectively. The spin-triplet gap is found to vanish over essentially the entire region $\kappa^{c}_{1}

We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings $J_{1}>0$ and $J_{2} \equiv \kappa J_{1}>0$, respectively, in the window $0 \leq \kappa \kappa^{{\rm cl}}$. This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case $\kappa = 0$ of the spin-$\frac{1}{2}$ model for the GS energy per spin, $E/N=-0.5521(2)J_{1}$, and the GS magnetic order parameter, $M=0.198(5)$ (in units where the classical value is $M^{{\rm cl}}=\frac{1}{2}$), which are among the best available. For the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ model we find that the classical transition at $\kappa=\kappa^{{\rm cl}}$ is split into two quantum phase transition at $\kappa^{c}_{1}=0.060(10)$ and $\kappa^{c}_{2}=0.165(5)$. The two quasiclassical AFM states (viz., the 120$^{\circ}$ N\'{e}el state and the striped state) are found to be the stable GS phases in the regime $\kappa \kappa^{c}_{2}$, respectively, while in the intermediate regimes $\kappa^{c}_{1}

We study the zero-temperature ground-state (GS) properties of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore, using the coupled cluster method (CCM) implemented to high orders of approximation. The system comprises a $J_{1}$--$J_{2}$ model on the checkerboard lattice, with isotropic Heisenberg interactions of strength $J_{1}$ between all nearest-neighbour pairs of spins on the square lattice, and of strength $J_{2}$ between half of the next-nearest-neighbour pairs (in the checkerboard pattern). We calculate results for the GS energy and average local GS on-site magnetization, using various antiferromagnetic classical ground states as CCM model states. We also give results for the susceptibility of one of these states against the formation of crossed-dimer valence-bond crystalline (CDVBC) ordering. The complete GS phase diagram is presented for arbitrary values of the frustration parameter $\kappa \equiv J_{2}/J_{1}$, and when each of the exchange couplings can take either sign.

Essay review of The Quantum World of Ultra-Cold Atoms and Light. Book I: Foundations of Quantum Optics, by C. Gardiner and P. Zoller, Singapore, World Scientific Publ. Co., 2014, xviii + 310 pp., £42.00 (paperback), ISBN 978-1-78326-461-2.

We study the J1-J1'-J2 quantum spin model on the two-dimensional square lattice using the coupled cluster method. We compare and contrast the influence of the interchain coupling J1' on the zero-temperature phase diagrams for the two spin values s = 1/2 and s = 1. Our most important result for the s = 1/2 case is the predicted existence of a quantum triple point (QTP) at (J1' ≈ 0.60 ± 0.03, J2 ≈ 0.33 ± 0.02) when J1 = 1. Below the QTP (J1'/J1 ≤ 0.60) we predict a second-order phase transition between the quasi-classical Neel and stripe-ordered phases, whereas the corresponding classical model, which contains only these two phases for all spin values s, yields a first-ordertransition. Above the QTP (J1'/J1 ≥ 0.60) an intermediate disordered phase emerges, which has no classical counterpart. By contrast, the situation for s = 1 is qualitatively different. Instead of a QTP where three phases co-exist, we now predict a quantum tricritical point at (J1' ≈ 0.66 ± 0.03, J2 ≈ 0.35 ± 0.02) when J1 = 1, where a line of second-order phase transitions between the quasi classical Neel and stripe-ordered phases (for J1'/J1 ≤ 0.66) meets a line of first-order phase transitions between the same two states (for J1'/J1 ≥ 0.66). Surprisingly, we find no evidence at all for any intermediate disordered phase in the s = 1 case.

The authors used the coupled cluster method (CCM) to investigate the evolution of the Rabi Hamiltonian from an initial state |0,| > composed of an empty field mode and an unexcited atom. Within the rotation-wave approxn. (RWA) the system would remain in this state indefinitely, since it is an eigenstate of the excitation no. N with corresponding eigenvalue zero. However, including of the otherwise neglected \"counter-rotating\" terms means that we allow \"energy non-conserving\" processes to occur, and their presence drives the temporal evolution of the Rabi system. The authors present results for the at. inversion and field occupation as function of time. They also show that no anti-bunching occurs, although the \"virtual\" processes do cause the field to become squeezed. [on SciFinder (R)]

We study the ground state and low-lying excited states in the nonlinear sigma model with the coupled cluster method of quantum many-body theory.

Quantum spins arranged on regular geometrical lattices, and interacting through a wide diversity of specified model Hamiltonians, provide a rich variety of magnetically ordered phases with many subtle properties. The zero-temperature quantum phase transitions between states of different order can be explored by the variation of internal control parameters within the interaction Hamiltonian. We illustrate how the systematic inclusion of multi-spin correlations for such lattice systems may be efficiently and effectively implemented via the coupled cluster method (CCM), which has been widely demonstrated on many previous occasions to be one of the most versatile methods of microscopic quantum many-body theory. Its power is illustrated by application to the spin-½ anisotropic Heisenberg (or XXZ) model on an infinite square lattice. The results obtained for such properties as the ground-state energy and sublattice magnetization are found to be as accurate as those obtained by any available alternative method. We show also how the CCM can now provide accurate ab initio estimates for the critical values of the parameters which mark the positions of phase boundaries between states of different quantum order, as well as for the critical indices associated with the singular behaviour near these transition points of various physical quantities.

Coherent mixed states (or thermal coherent states) associated with the displaced harmonic oscillator at finite temperature, are introduced as a 'random' (or 'thermal' or 'noisy') basis in Hilbert space. A resolution of the identity for these states is proved and used to generalize the usual coherent state formalism for the finite temperature case. The Bargmann representation of an operator is introduced and its relation to the P and Q representations is studied. Generalized P and Q representations for the finite temperature case are also considered and several interesting relations among them are derived.

We have applied the microscopic coupled-cluster method (CCM) of many-body quantum theory to the U(1) lattice gauge models in (1+1) and (2+1) dimensions. The mode couplings and plaquette correlations are studied in detail by means of a hierarchical truncation scheme. Good numerical results for the ground-state energy have been obtained for a range of coupling constants varying from strong to weak. The systematic and nonperturbative natures of the CCM are emphasized.

Rotavirus (RV) in stools of children

A reexamination of the center of mass problem for light systems in the context of coupled cluster theory has produced a new variational version of the method which is developed entirely in coordinate space. It involves independent cluster functions which depend only on the relative coordinates of the sub clusters of the system. In applications to the 4He nucleus described via a number of phenomenological and quasireaIistic microscopic Wigner potentials, the method is shown to be quantitatively rather accurate, producing in all cases almost exact results for the ground-state energies at the SUB(3) level of approximation.

In this work we discuss a series of calculations for the 4He nucleus which have been motivated by the coupled cluster method. For pedagogical reasons we restrict ourselves to the case of pure Wigner nucleon-nucleon interactions. All numerical work is done in the standard harmonic oscillator basis and with an exact treatment of the centre-of-mass motion. Particular emphasis is placed on elucidatingthe meaning of the coupled cluster wave function and its coordinate-space representation, as well as the relation with a variational-like use of the coupled cluster ansatz.