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

Temperature dependence of ESR intensity for the nanoscale molecular magnet V15

The electron spin resonance (ESR) of nanoscale molecular magnet ${\rm V}_{15}$ is studied. Since the Hamiltonian of ${\rm V}_{15}$ has a large Hilbert space and numerical calculations of the ESR signal evaluating the Kubo formula with exact diagonalization method is difficult, we implement the formula with the help of the random vector technique and the Chebyshev polynominal expansion, which we name the double Chebyshev expansion method. We calculate the temperature dependence of the ESR intensity of ${\rm V}_{15}$ and compare it with the data obtained in experiment. As another complementary approach, we also implement the Kubo formula with the subspace iteration method taking only important low-lying states into account. We study the ESR absorption curve below $100{\rm K}$ by means of both methods. We find that side peaks appear due to the Dzyaloshinsky-Moriya interaction and these peaks grows as temperature decreases.Comment: 9 pages, 4 figures. To appear in J. Phys. Soc. Jpn. Supp

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

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

An efficient scheme for numerical simulations of the spin-bath decoherence

We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of few coupled spins: (i) determining the pointer states of the system, and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For the problems of second type, the Chebyshev-based approach has been 3--4 times faster than the Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide spectrum of systems, with different spin baths and different Hamiltonians.Comment: 8 pages (RevTeX), 3 EPS figure

Superconductive "sodalite"-like clathrate calcium hydride at high pressures

Hydrogen-rich compounds hold promise as high-temperature superconductors under high pressures. Recent theoretical hydride structures on achieving high-pressure superconductivity are composed mainly of H2 fragments. Through a systematic investigation of Ca hydrides with different hydrogen contents using particle-swam optimization structural search, we show that in the stoichiometry CaH6 a body-centred cubic structure with hydrogen that forms unusual "sodalite" cages containing enclathrated Ca stabilizes above pressure 150 GPa. The stability of this structure is derived from the acceptance by two H2 of electrons donated by Ca forming a "H4" unit as the building block in the construction of the 3-dimensional sodalite cage. This unique structure has a partial occupation of the degenerated orbitals at the zone centre. The resultant dynamic Jahn-Teller effect helps to enhance electron-phonon coupling and leads to superconductivity of CaH6. A superconducting critical temperature (Tc) of 220-235 K at 150 GPa obtained from the solution of the Eliashberg equations is the highest among all hydrides studied thus far.Comment: 19 pages, 4 figure

Classification of singular Q-homology planes. I. Structure and singularities

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient singularity then it is a quotient of an affine cone over a projective curve by an action of a finite group respecting the set of lines through the vertex. In particular, it is contractible, has negative Kodaira dimension and only one singular point. We describe minimal normal completions of such planes.Comment: improved results from Ph.D. thesis (University of Warsaw, 2009), 25 pages, to appear in Israel J. Mat