Diagrammatic approach in the variational coupled-cluster method

Recently, as demonstrated by an antiferromagnetic spin-lattice application, we have successfully extended the coupled-cluster method (CCM) to a variational formalism in which two sets of distribution functions are introduced to evaluate Hamiltonian expectation. We calculated these distribution functions by employing an algebraic scheme. Here we present an alternative calculation based on a diagrammatic technique. Similar to the method of correlated-basis functionals (CBF), a generating functional is introduced and calculated by a linked-cluster expansion in terms of diagrams which are categorized and constructed according to a few simple rules and using correlation coefficients and Pauli exclusion principle (or Pauli line) as basic elements. Infinite resummations of diagrams can then be done in a straightforward manner. One such resummation, which includes all so-called ring diagrams and ignores Pauli exclusion principle, reproduces spin-wave theory (SWT). Approximations beyond SWT are also given. Interestingly, one such approximation including all so-called super-ring diagrams by a resummation of infinite Pauli lines in additional to resummations of ring diagrams produces a convergent, precise number for the order-parameter of the one-dimensional isotropic model, contrast to the well-known divergence of SWT. We also discuss the direct relation between our variational CCM and CBF and discuss a possible unification of the two theories.Comment: 18 pages, 9 figure

Longitudinal excitations in quantum antiferromagnets

By extending our recently proposed magnon-density-waves to low dimensions, we investigate, using a microscopic many-body approach, the longitudinal excitations of the quasi-one-dimensional (quasi-1d) and quasi-2d Heisenberg antiferromagnetic systems on a bipartite lattice with a general spin quantum number. We obtain the full energy spectrum of the longitudinal mode as a function of the coupling constants in the original lattice Hamiltonian and find that it always has a non-zero energy gap if the ground state has a long-range order and becomes gapless for the pure isotropic 1d model. The numerical value of the minimum gap in our approximation agrees with that of a longitudinal mode observed in the quasi-1d antiferromagnetic compound KCuF${}_3$ at low temperature. It will be interesting to compare values of the energy spectrum at other momenta if their experimental results are available.Comment: 19 pages, 4 figure

Excited states of quantum many-body interacting systems: A variational coupled-cluster description

We extend recently proposed variational coupled-cluster method to describe excitation states of quantum many-body interacting systems. We discuss, in general terms, both quasiparticle excitations and quasiparticle-density-wave excitations (collective modes). In application to quantum antiferromagnets, we reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of spin $\pm 1$. In addition, we obtain new, spin-zero magnon-density-wave excitations which has been missing in Anserson's spin-wave theory. Implications of these new collective modes are discussed.Comment: 17 pages, 4 figure

The K−p→Σ0π0K^-p\to \Sigma^0\pi^0 reaction at low energies in a chiral quark model

A chiral quark-model approach is extended to the study of the $\bar{K}N$ scattering at low energies. The process of $K^-p\to \Sigma^0\pi^0$ at $P_K\lesssim 800$ MeV/c (i.e. the center mass energy $W\lesssim 1.7$ GeV) is investigated. This approach is successful in describing the differential cross sections and total cross section with the roles of the low-lying $\Lambda$ resonances in $n=1$ shells clarified. The $\Lambda(1405)S_{01}$ dominates the reactions over the energy region considered here. Around $P_K\simeq 400$ MeV/c, the $\Lambda(1520)D_{03}$ is responsible for a strong resonant peak in the cross section. The $\Lambda(1670)S_{01}$ has obvious contributions around $P_K=750$ MeV/c, while the contribution of $\Lambda(1690)D_{03}$ is less important in this energy region. The non-resonant background contributions, i.e. $u$-channel and $t$-channel, also play important roles in the explanation of the angular distributions due to amplitude interferences.Comment: 18 pages and 7 figure

Two-dimensional Poisson Trees converge to the Brownian web

The Brownian web can be roughly described as a family of coalescing one-dimensional Brownian motions starting at all times in $\R$ and at all points of $\R$. It was introduced by Arratia; a variant was then studied by Toth and Werner; another variant was analyzed recently by Fontes, Isopi, Newman and Ravishankar. The two-dimensional \emph{Poisson tree} is a family of continuous time one-dimensional random walks with uniform jumps in a bounded interval. The walks start at the space-time points of a homogeneous Poisson process in $\R^2$ and are in fact constructed as a function of the point process. This tree was introduced by Ferrari, Landim and Thorisson. By verifying criteria derived by Fontes, Isopi, Newman and Ravishankar, we show that, when properly rescaled, and under the topology introduced by those authors, Poisson trees converge weakly to the Brownian web.Comment: 22 pages, 1 figure. This version corrects an error in the previous proof. The results are the sam

Ballistic Thermal Rectification in Asymmetric Three-Terminal Mesoscopic Dielectric Systems

By coupling the asymmetric three-terminal mesoscopic dielectric system with a temperature probe, at low temperature, the ballistic heat flux flow through the other two asymmetric terminals in the nonlinear response regime is studied based on the Landauer formulation of transport theory. The thermal rectification is attained at the quantum regime. It is a purely quantum effect and is determined by the dependence of the ratio $\tau_{RC}(\omega)/\tau_{RL}(\omega)$ on $\omega$, the phonon's frequency. Where $\tau_{RC}(\omega)$ and $\tau_{RL}(\omega)$ are respectively the transmission coefficients from two asymmetric terminals to the temperature probe, which are determined by the inelastic scattering of ballistic phonons in the temperature probe. Our results are confirmed by extensive numerical simulations.Comment: 10 pages, 4 figure

On a property of random-oriented percolation in a quadrant

Grimmett's random-orientation percolation is formulated as follows. The square lattice is used to generate an oriented graph such that each edge is oriented rightwards (resp. upwards) with probability $p$ and leftwards (resp. downwards) otherwise. We consider a variation of Grimmett's model proposed by Hegarty, in which edges are oriented away from the origin with probability $p$, and towards it with probability $1-p$, which implies rotational instead of translational symmetry. We show that both models could be considered as special cases of random-oriented percolation in the NE-quadrant, provided that the critical value for the latter is 1/2. As a corollary, we unconditionally obtain a non-trivial lower bound for the critical value of Hegarty's random-orientation model. The second part of the paper is devoted to higher dimensions and we show that the Grimmett model percolates in any slab of height at least 3 in $\mathbb{Z}^3$.Comment: The abstract has been updated, discussion has been added to the end of the articl