Calculating response functions in time domain with non-orthonormal basis sets

We extend the recently proposed order-N algorithms (cond-mat/9703224) for calculating linear- and nonlinear-response functions in time domain to the systems described by nonorthonormal basis sets.Comment: 4 pages, no figure

Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices

A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind encountered in quantum physics the memory and CPU requirements of this method scale linearly with the dimension of the matrix. We derive a rigorous estimate of the statistical error, supporting earlier observations that the computational efficiency of this approach increases with matrix size. We use this method and an imaginary-time version of it to compute the energy and the specific heat of three different, exactly solvable, spin-1/2 models and compare with the exact results to study the dependence of the statistical errors on sample and matrix size.Comment: 24 pages, 24 figure

Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate

We introduce an efficient and numerically stable method for calculating linear response functions $\chi(\vec{q},\omega)$ of quantum systems at finite temperatures. The method is a combination of numerical solution of the time-dependent Schroedinger equation, random vector representation of trace, and Chebyshev polynomial expansion of Boltzmann operator. This method should be very useful for a wide range of strongly correlated quantum systems at finite temperatures. We present an application to the ESR spectrum of s=1/2 antiferromagnet Cu benzoate.Comment: 4 pages, 4 figure

Solid helium at high pressure: A path-integral Monte Carlo simulation

Solid helium (3He and 4He) in the hcp and fcc phases has been studied by path-integral Monte Carlo. Simulations were carried out in the isothermal-isobaric (NPT) ensemble at pressures up to 52 GPa. This allows one to study the temperature and pressure dependences of isotopic effects on the crystal volume and vibrational energy in a wide parameter range. The obtained equation of state at room temperature agrees with available experimental data. The kinetic energy, E_k, of solid helium is found to be larger than the vibrational potential energy, E_p. The ratio E_k/E_p amounts to about 1.4 at low pressures, and decreases as the applied pressure is raised, converging to 1, as in a harmonic solid. Results of these simulations have been compared with those yielded by previous path integral simulations in the NVT ensemble. The validity range of earlier approximations is discussed.Comment: 7 pages, 5 figure

Direct perturbation theory on the shift of Electron Spin Resonance

We formulate a direct and systematic perturbation theory on the shift of the main paramagnetic peak in Electron Spin Resonance, and derive a general expression up to second order. It is applied to one-dimensional XXZ and transverse Ising models in the high field limit, to obtain explicit results including the polarization dependence for arbitrary temperature.Comment: 5 pages (no figures) in REVTE

Quantum Dynamics of Spin Wave Propagation Through Domain Walls

Through numerical solution of the time-dependent Schrodinger equation, we demonstrate that magnetic chains with uniaxial anisotropy support stable structures, separating ferromagnetic domains of opposite magnetization. These structures, domain walls in a quantum system, are shown to remain stable if they interact with a spin wave. We find that a domain wall transmits the longitudinal component of the spin excitations only. Our results suggests that continuous, classical spin models described by LLG equation cannot be used to describe spin wave-domain wall interaction in microscopic magnetic systems

Fast algorithm for calculating two-photon absorption spectra

We report a numerical calculation of the two-photon absorption coefficient of electrons in a binding potential using the real-time real-space higher-order difference method. By introducing random vector averaging for the intermediate state, the task of evaluating the two-dimensional time integral is reduced to calculating two one-dimensional integrals. This allows the reduction of the computation load down to the same order as that for the linear response function. The relative advantage of the method compared to the straightforward multi-dimensional time integration is greater for the calculation of non-linear response functions of higher order at higher energy resolution.Comment: 4 pages, 2 figures. It will be published in Phys. Rev. E on 1, March, 199

First Principles Calculation of Elastic Properties of Solid Argon at High Pressures

The density and the elastic stiffness coefficients of fcc solid argon at high pressures from 1 GPa up to 80 GPa are computed by first-principles pseudopotential method with plane-wave basis set and the generalized gradient approximation (GGA). The result is in good agreement with the experimental result recently obtained with the Brillouin spectroscopy by Shimizu et al. [Phys. Rev. Lett. 86, 4568 (2001)]. The Cauchy condition was found to be strongly violated as in the experimental result, indicating large contribution from non-central many-body force. The present result has made it clear that the standard density functional method with periodic boundary conditions can be successfully applied for calculating elastic properties of rare gas solids at high pressures in contrast to those at low pressures where dispersion forces are important.Comment: 4 pages, 5 figures, submitted to PR

Origin of the Canonical Ensemble: Thermalization with Decoherence

We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced density matrix to a fully decoherent state, and furthermore the diagonal elements of the reduced density matrix approach those expected for the system in the canonical ensemble. We show one exception to the normal case is if the spin system cannot exchange energy with the spin bath. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the canonical ensemble is a state that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics.Comment: 12 pages, 4 figures, accepted for publication by J. Phys. Soc. Jp