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

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

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

On the near-threshold pˉp\bar pp invariant mass spectrum measured in J/ψJ/\psi and ψ′\psi' decays

A systematic analysis of the near-threshold enhancement in the $\bar pp$ invariant mass spectrum seen in the decay reactions $J/\psi \to x \bar pp$ and $\psi (3686) \to x \bar pp$ $(x = \gamma,\, \omega,\, \rho,\, \pi,\, \eta)$ is presented. The enhancement is assumed to be due to the $\bar NN$ final-state interaction (FSI) and the pertinent FSI effects are evaluated in an approach that is based on the distorted-wave Born approximation. For the $\bar NN$ interaction a recent potential derived within chiral effective field theory and fitted to results of a partial-wave analysis of $\bar pp$ scattering data is considered and, in addition, an older phenomenological model constructed by the J\"ulich group. It is shown that the near-threshold spectrum observed in various decay reactions can be reproduced simultaneously and consistently by our treatment of the $\bar pp$ FSI. It turns out that the interaction in the isospin-1 $^1S_0$ channel required for the description of the $J/\psi \to \gamma \bar pp$ decay predicts a $\bar NN$ bound state.Comment: 13 pages, 12 figure

On AdS to dS transitions in higher-curvature gravity

We study the possible existence of gravitational phase transitions from AdS to dS geometries in the context of higher-curvature gravities. We use Lanczos-Gauss-Bonnet (LGB) theory with a positive cosmological constant as a toy model. This theory has two maximally symmetric vacua with positive (dS) and negative (AdS) constant curvature. We show that a phase transition from the AdS vacuum to a dS black hole geometry takes place when the temperature reaches a critical value. The transition is produced by nucleation of bubbles of the new phase that expand afterwards. We claim that this phenomenon is not particular to the model under study, and shall also be part of generic gravitational theories with higher-curvature terms.Comment: 12 pages, 3 figures; v2: comments and references adde

Iron(III) bromide catalyzed bromination of 2-tert-butylpyrene and corresponding position-dependent aryl-functionalized pyrene derivatives

The present work probes the bromination mechanism of 2-tert-butylpyrene (1), which regioselectively affords mono-, di-, tri- and tetra-bromopyrenes, by theoretical calculation and detailed experimental methods. The bromine atom may be directed to the K-region (positions 5- and 9-) instead of the more reactive 6- and 8-positions in the presence of iron powder. In this process, FeBr₃ plays a significant role to release steric hindrance or lower the activation energy of the rearrangement. The intermediate bromopyrene derivatives were isolated and confirmed by ¹H NMR spectrometry, mass spectroscopy and elemental analysis. Further evidence on substitution position originated from a series of aryl substituted pyrene derivatives, which were obtained from the corresponding bromopyrenes on reaction with 4-methoxy-phenylboronic acid by a Suzuki–Miyaura cross-coupling reaction. All position-dependent aryl-functionalized pyrene derivatives are characterized by single X-ray diffraction, ¹H/¹³C NMR, FT-IR and MS, and offered straightforward evidence to support our conclusion. Furthermore, the photophysical properties of a series of compounds were confirmed by fluorescence and absorption, as well as by fluorescence lifetime measurements