Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O$(3)$ symmetry) displays the inductor $\sigma (\omega) =(i\omega L)^{-1}$ and capacitor $i \omega C$ behaviors for the ordered and disordered phases, respectively. Both constants, $C$ and $L$, have the same scaling dimension as that of the reciprocal paramagnetic gap $\Delta^{-1}$. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O$(2)$ case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap $\Delta$ directly. Thereby, the set of critical amplitude ratios as to $C$, $L$ and $\Delta$ are estimated with the finite-size-scaling analysis for the cluster with $N \le 34$ spins

Numerical diagonalization analysis of the ground-state superfluid-localization transition in two dimensions

Ground state of the two-dimensional hard-core-boson system in the presence of the quenched random chemical potential is investigated by means of the exact-diagonalization method for the system sizes up to L=5. The criticality and the DC conductivity at the superfluid-localization transition have been controversial so far. We estimate, with the finite-size scaling analysis, the correlation-length and the dynamical critical exponents as nu=2.3(0.6) and z=2, respectively. The AC conductivity is computed with the Gagliano-Balseiro formula, with which the resolvent (dynamical response function) is expressed in terms of the continued-fraction form consisted of Lanczos tri-diagonal elements. Thereby, we estimate the universal DC conductivity as sigma_c(omega=0)=0.135(0.01) ((2e)^2/h)

Asymptotic theory of semiparametric ZZ-estimators for stochastic processes with applications to ergodic diffusions and time series

This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to derive the asymptotic behavior of the solution to an estimating equation $\theta\leadsto \Psi_n(\theta,\widehat{h}_n)=0$ with an abstract nuisance parameter $h$ when the compensator of $\Psi_n$ is random. As its application, we consider the estimation problem in an ergodic diffusion process model where the drift coefficient contains an unknown, finite-dimensional parameter $\theta$ and the diffusion coefficient is indexed by a nuisance parameter $h$ from an infinite-dimensional space. An example for the nuisance parameter space is a class of smooth functions. We establish the asymptotic normality and efficiency of a $Z$-estimator for the drift coefficient. As another application, we present a similar result also in an ergodic time series model.Comment: Published in at http://dx.doi.org/10.1214/09-AOS693 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Folding of the triangular lattice in a discrete three-dimensional space: Density-matrix-renormalization-group study

Folding of the triangular lattice in a discrete three-dimensional space is investigated numerically. Such ``discrete folding'' has come under through theoretical investigation, since Bowick and co-worker introduced it as a simplified model for the crumpling of the phantom polymerized membranes. So far, it has been analyzed with the hexagon approximation of the cluster variation method (CVM). However, the possible systematic error of the approximation was not fully estimated; in fact, it has been known that the transfer-matrix calculation is limited in the tractable strip widths L \le 6. Aiming to surmount this limitation, we utilized the density-matrix renormalization group. Thereby, we succeeded in treating strip widths up to L=29 which admit reliable extrapolations to the thermodynamic limit. Our data indicate an onset of a discontinuous crumpling transition with the latent heat substantially larger than the CVM estimate. It is even larger than the latent heat of the planar (two dimensional) folding, as first noticed by the preceding CVM study. That is, contrary to our naive expectation, the discontinuous character of the transition is even promoted by the enlargement of the embedding-space dimensions. We also calculated the folding entropy, which appears to lie within the best analytical bound obtained previously via combinatorics arguments