Thermodynamic properties of the one-dimensional Kondo insulators studied by the density matrix renormalization group method

Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and specific heat are calculated down to T=0.1t for various exchange constants. The obtained results clearly show crossover behavior from the high temperature regime of nearly independent localized spins and conduction electrons to the low temperature regime where the two degrees of freedom couple strongly. The low temperature energy scales of the charge and spin susceptibilities are determined and shown to be equal to the quasiparticle gap and the spin gap, respectively, for weak exchange couplings.Comment: 4 pages, 3 Postscript figures, REVTeX, submitted to J. Phys. Soc. Jp

Thermodynamics of doped Kondo insulator in one dimension: Finite Temperature DMRG Study

The finite-temperature density-matrix renormalization-group method is applied to the one-dimensional Kondo lattice model near half filling to study its thermodynamics. The spin and charge susceptibilities and entropy are calculated down to T=0.03t. We find two crossover temperatures near half filling. The higher crossover temperature continuously connects to the spin gap at half filling, and the susceptibilities are suppressed around this temperature. At low temperatures, the susceptibilities increase again with decreasing temperature when doping is finite. We confirm that they finally approach to the values obtained in the Tomonaga-Luttinger (TL) liquid ground state for several parameters. The crossover temperature to the TL liquid is a new energy scale determined by gapless excitations of the TL liquid. The transition from the metallic phase to the insulating phase is accompanied by the vanishing of the lower crossover temperature.Comment: 4 pages, 7 Postscript figures, REVTe

Lorentz Covariance and the Dimensional Crossover of 2d-Antiferromagnets

We derive a lattice $\beta$-function for the 2d-Antiferromagnetic Heisenberg model, which allows the lattice interaction couplings of the nonperturbative Quantum Monte Carlo vacuum to be related directly to the zero-temperature fixed points of the nonlinear sigma model in the presence of strong interplanar and spin anisotropies. In addition to the usual renormalization of the gapful disordered state in the vicinity of the quantum critical point, we show that this leads to a chiral doubling of the spectra of excited states

Possible explanation for star-crushing effect in binary neutron star simulations

A possible explanation is suggested for the controversial star-crushing effect seen in numerical simulations of inspiraling neutron star binaries by Wilson, Mathews and Marronetti (WMM). An apparently incorrect definition of momentum density in the momentum constraint equation used by WMM gives rise to a post-1-Newtonian error in the approximation scheme. We show by means of an analytic, post-1-Newtonian calculation that this error causes an increase of the stars' central densities which is of the order of several percent when the stars are separated by a few stellar radii, in agreement with what is seen in the simulations.Comment: 4 pages, 1 figure, uses revetx macros, minor revision

Statistical Aspects of Model Selection

Various aspects of statistical model selection are discussed from the view point of a statistician. Our concern here is about selection procedures based on the Kullback Leibler information number. Derivation of AIC (Akaike's Information Criterion) is given. As a result a natural extension of AIC, called TIC (Takeuchi's Information Criterion) follows. It is shown that the TIC is asymptotically equivalent to Cross Validation in a general context, although AIC is asymptotically equivalent only for the case of independent identically distributed observations. Next, the maximum penalized likelihood estimate is considered in place of the maximum likelihood estimate as an estimation of parameters after a model is selected. Then the weight of penalty is also the one to be selected. We will show that, starting from the same Kullback-Leibler information number, a useful criterion RIC (Regularization Information Criterion) is derived to select both the model and the weight of penalty. This criterion is in fact an extension of TIC as well, as of AIC. Comparison of various criteria, including consistency and efficiency is summarized in Section 5. Applications of such criteria to time series models are given in the last section

Merger of binary neutron stars of unequal mass in full general relativity

We present results of three dimensional numerical simulations of the merger of unequal-mass binary neutron stars in full general relativity. A $\Gamma$-law equation of state $P=(\Gamma-1)\rho\epsilon$ is adopted, where $P$, $\rho$, \varep, and $\Gamma$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant, respectively. We take $\Gamma=2$ and the baryon rest-mass ratio $Q_M$ to be in the range 0.85--1. The typical grid size is $(633,633,317)$ for $(x,y,z)$ . We improve several implementations since the latest work. In the present code, the radiation reaction of gravitational waves is taken into account with a good accuracy. This fact enables us to follow the coalescence all the way from the late inspiral phase through the merger phase for which the transition is triggered by the radiation reaction. It is found that if the total rest-mass of the system is more than $\sim 1.7$ times of the maximum allowed rest-mass of spherical neutron stars, a black hole is formed after the merger irrespective of the mass ratios. The gravitational waveforms and outcomes in the merger of unequal-mass binaries are compared with those in equal-mass binaries. It is found that the disk mass around the so formed black holes increases with decreasing rest-mass ratios and decreases with increasing compactness of neutron stars. The merger process and the gravitational waveforms also depend strongly on the rest-mass ratios even for the range $Q_M= 0.85$--1.Comment: 32 pages, PRD68 to be publishe

Gravitational waves from axisymmetrically oscillating neutron stars in general relativistic simulations

Gravitational waves from oscillating neutron stars in axial symmetry are studied performing numerical simulations in full general relativity. Neutron stars are modeled by a polytropic equation of state for simplicity. A gauge-invariant wave extraction method as well as a quadrupole formula are adopted for computation of gravitational waves. It is found that the gauge-invariant variables systematically contain numerical errors generated near the outer boundaries in the present axisymmetric computation. We clarify their origin, and illustrate it possible to eliminate the dominant part of the systematic errors. The best corrected waveforms for oscillating and rotating stars currently contain errors of magnitude $\sim 10^{-3}$ in the local wave zone. Comparing the waveforms obtained by the gauge-invariant technique with those by the quadrupole formula, it is shown that the quadrupole formula yields approximate gravitational waveforms besides a systematic underestimation of the amplitude of $O(M/R)$ where $M$ and $R$ denote the mass and the radius of neutron stars. However, the wave phase and modulation of the amplitude can be computed accurately. This indicates that the quadrupole formula is a useful tool for studying gravitational waves from rotating stellar core collapse to a neutron star in fully general relativistic simulations. Properties of the gravitational waveforms from the oscillating and rigidly rotating neutron stars are also addressed paying attention to the oscillation associated with fundamental modes