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

Chemical modification of poly(p-phenylene) for use in ablative compositions

Development of ablative materials based on modification of polyphenylene compounds is discussed. Chemical and physical properties are analyzed for application as heat resistant materials. Synthesis of linear polyphenylenes is described. Effects of exposure to oxyacetylene flame and composition of resultant char layer are presented

The permutation group S_N and large Nc excited baryons

We study the excited baryon states for an arbitrary number of colors Nc from the perspective of the permutation group S_N of N objects. Classifying the transformation properties of states and quark-quark interaction operators under S_N allows a general analysis of the spin-flavor structure of the mass operator of these states, in terms of a few unknown constants parameterizing the unknown spatial structure. We explain how to perform the matching calculation of a general two-body quark-quark interaction onto the operators of the 1/Nc expansion. The inclusion of core and excited quark operators is shown to be necessary. Considering the case of the negative parity L=1 states transforming in the MS of S_N, we discuss the matching of the one-gluon and the Goldstone-boson exchange interactions.Comment: 38 pages. Final version to be published in Physical Review

Electron Spin Resonance of SrCu2(BO3)2 at High Magnetic Field

We calculate the electron spin resonance (ESR) spectra of the quasi-two-dimensional dimer spin liquid SrCu2(BO3)2 as a function of magnetic field B. Using the standard Lanczos method, we solve a Shastry-Sutherland Hamiltonian with additional Dzyaloshinsky-Moriya (DM) terms which are crucial to explain different qualitative aspects of the ESR spectra. In particular, a nearest-neighbor DM interaction with a non-zero D_z component is required to explain the low frequency ESR lines for B || c. This suggests that crystal symmetry is lowered at low temperatures due to a structural phase transition.Comment: 4 pages, 4 b&w figure

Distribution functions in percolation problems

Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of such distribution functions in the limits where certain scaling variables become small or large. Our study includes the pair-connection probability, the distributions of the fractal masses of the backbone, the red bonds and the shortest, the longest and the average self-avoiding walk between any two points on a cluster, as well as the distribution of the total resistance in the random resistor network. Our analysis draws solely on general, structural features of the underlying diagrammatic perturbation theory, and hence our main results are valid to arbitrary loop order.Comment: 15 pages, 1 figur

Detecting Hidden Differences via Permutation Symmetries

We present a method for describing and characterizing the state of N particles that may be distinguishable in principle but not in practice due to experimental limitations. The technique relies upon a careful treatment of the exchange symmetry of the state among experimentally accessible and experimentally inaccessible degrees of freedom. The approach we present allows a new formalisation of the notion of indistinguishability and can be implemented easily using currently available experimental techniques. Our work is of direct relevance to current experiments in quantum optics, for which we provide a specific implementation.Comment: 8 pages, 1 figur

Equilibrium counterfactuals

We incorporate structural modellers into the economy they model. Using traditional moment-matching, they treat policy changes as zero probability (or exogenous) ”counterfactuals.” Bias occurs since real-world agents understand policy changes are positive probability events guided by modellers. Downward, upward, or sign bias occurs. Bias is illustrated by calibrating the Leland model to the 2017 tax cut. The traditional identifying assumption, constant moment partial derivative sign, is incorrect with policy optimization. The correct assumption is constant moment total derivative sign accounting for estimation-policy feedback. Model agent expectations can be updated iteratively until policy advice converges to agent expectations, with bias vanishing

The Isovector Quadrupole-Quadrupole Interaction Used in Shell Model Calculations

An interaction $-\chi Q\cdot Q(1+B\vec{\tau}(1)\cdot \vec{\tau}(2))$ is used in a shell model calculation for $^{10}Be$. Whereas for $B=0$ the $2_1^+$ state is two-fold degenerate, introducing a negative $B$ causes an `isovector' $2^+$ state to come down to zero energy at $B=-0.67$ and an $S=1~L=1$ triplet ($J=0^+,~1^+,~2^+$) to come down to zero energy at $B=-0.73$. These are undesirable properties, but a large negative $B$ is apparently needed to fit the energy of the isovector giant quadrupole resonance.Comment: 12 pages, revtex, 2 figures (available on request