Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies and correlation functions of the Bose Hubbard model is developed. We illustrate the general formalism, which includes all possible inhomogeneous effects in the formalism, such as disorder, or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third-order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator to superfluid transition along with a generalization of the RPA-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions; the accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling theory results are benchmarked against numerically exact QMC simulations in two and three dimensions and against DMRG calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.Comment: 48 pages 14 figures RevTe

Geometrical Aspects on Parameter estimation of stochastic gravitational wave background: beyond the Fisher analysis

The maximum likelihood method is often used for parameter estimation in gravitational wave astronomy. Recently, an interesting approach was proposed by Vallisneri to evaluate the distributions of parameter estimation errors expected for the method. This approach is to statistically analyze the local peaks of the likelihood surface, and works efficiently even for signals with low signal-to-noise ratios. Focusing special attention to geometric structure of the likelihood surface, we follow the proposed approach and derive formulae for a simplified model of data analysis where the target signal has only one intrinsic parameter, along with its overall amplitude. Then we apply our formulae to correlation analysis of stochastic gravitational wave background with a power-law spectrum. We report qualitative trends of the formulae using numerical results specifically obtained for correlation analysis with two Advanced-LIGO detectors.Comment: 23 pages, to be published in PR

Axiomatic Bargaining Theory on Opportunity Assignments

This paper discusses issues of axiomatic bargaining problems over opportunity assignments. The fair arbitrator uses the principle of "equal opportunity" for all players to make the recommendation on re- source allocations. A framework in such a context is developed and several classical solutions to standard bargaining problems are reformulated and axiomatically characterized. Working Paper 06-4

Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems

Recently, Syljuasen and Sandvik proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a given model. Based on their framework, we propose an algorithm that is a natural extension of the conventional loop algorithm with the split-spin representation. A complete table of the vertex density and the worm-scattering probability is presented for the general XXZ model of an arbitrary S with a uniform magnetic field.Comment: 12 pages, 7 figures, insert a word "squared" in the first line of the caption of Fig.7 and correct the label of vertical axis of Fig.

Moduli Space Dimensions of Multi-Pronged Strings

The numbers of bosonic and fermionic zero modes of multi-pronged strings are counted in ${\cal N}=4$ super-Yang-Mills theory and compared with those of the IIB string theory. We obtain a nice agreement for the fermionic zero modes, while our result for the bosonic zero modes differs from that obtained in the IIB string theory. The possible origin of the discrepancy is discussedComment: 15 pages, 2 figure

Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction

Through Quantum Monte Carlo simulation, we study the biquadratic-interaction model with the SU(2) symmetry in two and three dimensions. The zero-temperature phase diagrams for the two cases are identical and exhibit an intermediate phase characterized by finite quadrupole moment, in agreement with mean-field type arguments and the semi-classical theory. In three dimensions, we demonstrate that the model in the quadrupolar regime has a phase transition at a finite temperature. In contrast to predictions by mean-field theories, the phase transition to the quadrupolar phase turns out to be of the second order. We also examine the critical behavior in the two marginal cases with the SU(3) symmetry.Comment: 4 pages 5 figure

The axial anomaly and the phases of dense QCD

The QCD axial anomaly, by coupling the chiral condensate and BCS pairing fields of quarks in dense matter, leads to a new critical point in the QCD phase diagram \cite{HTYB,chiral2}, which at sufficiently low temperature should terminate the line of phase transitions between chirally broken hadronic matter and color superconducting quark matter. The critical point indicates that matter at low temperature should cross over smoothly from the hadronic to the quark phase, as suggested earlier on the basis of symmetry. We review here the arguments, based on a general Ginzburg-Landau effective Lagrangian, for the existence of the new critical point, as well as discuss possible connections between the QCD phase structure and the BEC-BCS crossover in ultracold trapped atomic fermion systems at unitarity. and implications for the presence of quark matter in neutron stars.Comment: 8 pages, Proceedings of Quark Matter 2008, Jaipu

Securing Basic Well-being for All

The purpose of this paper is to examine the possibility of a social choice rule to implement a social policy for securing basic well-being for all. The paper introduces a new scheme of social choice, called a social relation function (SRF), which associates a reflexive and transitive binary relation over a set of social policies to each profile of individual well-being appraisals and each profile of group evaluations. As part of the domains of SRFs, the available class of group evaluations is constrained by three conditions. Furthermore, the non-negative response (NR) and the weak Pareto condition (WP) are introduced. NR demands giving priority to group evaluation, while treating the groups as formally equal relative to each other. WP requires treating impartially the well-being appraisals of all individuals. In conclusion, this paper shows that under some reasonable assumptions, there exists an SRF that satisfies NR and WP

Spin fluctuations in CuGeO3_3 probed by light scattering

We have measured temperature dependence of low-frequency Raman spectra in CuGeO$_3$, and have observed the quasi-elastic scattering in the $(c,c)$ polarization above the spin-Peierls transition temperature. We attribute it to the fluctuations of energy density in the spin system. The magnetic specific heat and an inverse of the magnetic correlation length can be derived from the quasi-elastic scattering. The inverse of the magnetic correlation length is proportional to $(T-T_{SP})^{1/2}$ at high temperatures. We compare the specific heat with a competing-$J$ model. This model cannot explain quantitatively both the specific heat and the magnetic susceptibility with the same parameters. The origin of this discrepancy is discussed.Comment: 17 pages, REVTeX, 5 Postscript figures; in press in PR

Universal relations in the finite-size correction terms of two-dimensional Ising models

Quite recently, Izmailian and Hu [Phys. Rev. Lett. 86, 5160 (2001)] studied the finite-size correction terms for the free energy per spin and the inverse correlation length of the critical two-dimensional Ising model. They obtained the universal amplitude ratio for the coefficients of two series. In this study we give a simple derivation of this universal relation; we do not use an explicit form of series expansion. Moreover, we show that the Izmailian and Hu's relation is reduced to a simple and exact relation between the free energy and the correlation length. This equation holds at any temperature and has the same form as the finite-size scaling.Comment: 4 pages, RevTeX, to appear in Phys. Rev. E, Rapid Communication