Spin dynamics of an ultra-small nanoscale molecular magnet

We present mathematical transformations which allow us to calculate the spin dynamics of an ultra-small nanoscale molecular magnet consisting of a dimer system of classical (high) Heisenberg spins. We derive exact analytic expressions (in integral form) for the time-dependent spin autocorrelation function and several other quantities. The properties of the time-dependent spin autocorrelation function in terms of various coupling parameters and temperature are discussed in detail

Exact time correlation functions for N classical Heisenberg spins in the `squashed' equivalent neighbor model

We present exact integral representations of the time-dependent spin-spin correlation functions for the classical Heisenberg N-spin `squashed' equivalent neighbor model, in which one spin is coupled via the Heisenberg exchange interaction with strength $J_1$ to the other N-1 spins, each of which is coupled via the Heisenberg exchange coupling with strength $J_2$ to the remaining N-2 spins. At low temperature T we find that the N spins oscillate in four modes, one of which is a central peak for a semi-infinite range of the values of the exchange coupling ratio. For the N=4 case of four spins on a squashed tetrahedron, detailed numerical evaluations of these results are presented. As $T\to\infty$, we calculate exactly the long-time asymptotic behavior of the correlation functions for arbitrary N, and compare our results with those obtained for three spins on an isosceles triangle.Comment: 9 pages, 8 figures, submitted to Phys. Rev.

Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations

A variety of recent experiments probing the low-temperature transport properties of quantum Hall systems have suggested an interpretation in terms of liquid crystalline mesophases dubbed {\em quantum Hall liquid crystals}. The single mode approximation (SMA) has been a useful tool for the determination of the excitation spectra of various systems such as phonons in $^4$He and in the fractional quantum Hall effect. In this paper we calculate (via the SMA) the spectrum of collective excitations in a quantum Hall liquid crystal by considering {\em nematic}, {\em tetratic}, and {\em hexatic} generalizations of Laughlin's trial wave function having two-, four- and six-fold broken rotational symmetry, respectively. In the limit of zero wavevector \qq the dispersion of these modes is singular, with a gap that is dependent on the direction along which \qq=0 is approached for {\em nematic} and {\em tetratic} liquid crystalline states, but remains regular in the {\em hexatic} state, as permitted by the fourth order wavevector dependence of the (projected) oscillator strength and static structure factor.Comment: 6 pages, 5 eps figures include

Covalency effects on the magnetism of EuRh2P2

In experiments, the ternary Eu pnictide EuRh2P2 shows an unusual coexistence of a non-integral Eu valence of about 2.2 and a rather high Neel temperature of 50 K. In this paper, we present a model which explains the non-integral Eu valence via covalent bonding of the Eu 4f-orbitals to P2 molecular orbitals. In contrast to intermediate valence models where the hybridization with delocalized conduction band electrons is known to suppress magnetic ordering temperatures to at most a few Kelvin, covalent hybridization to the localized P2 orbitals avoids this suppression. Using perturbation theory we calculate the valence, the high temperature susceptibility, the Eu single-ion anisotropy and the superexchange couplings of nearest and next-nearest neighbouring Eu ions. The model predicts a tetragonal anisotropy of the Curie constants. We suggest an experimental investigation of this anisotropy using single crystals. From experimental values of the valence and the two Curie constants, the three free parameters of our model can be determined.Comment: 9 pages, 5 figures, submitted to J. Phys.: Condens. Matte

A Fundamental Theorem on the Structure of Symplectic Integrators

I show that the basic structure of symplectic integrators is governed by a theorem which states {\it precisely}, how symplectic integrators with positive coefficients cannot be corrected beyond second order. All previous known results can now be derived quantitatively from this theorem. The theorem provided sharp bounds on second-order error coefficients explicitly in terms of factorization coefficients. By saturating these bounds, one can derive fourth-order algorithms analytically with arbitrary numbers of operators.Comment: 4 pages, no figure

Short time evolved wave functions for solving quantum many-body problems

The exact ground state of a strongly interacting quantum many-body system can be obtained by evolving a trial state with finite overlap with the ground state to infinite imaginary time. In this work, we use a newly discovered fourth order positive factorization scheme which requires knowing both the potential and its gradients. We show that the resultaing fourth order wave function alone, without further iterations, gives an excellent description of strongly interacting quantum systems such as liquid 4He, comparable to the best variational results in the literature.Comment: 5 pages, 3 figures, 1 tabl

Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies

We study a one-dimensional system composed of three charged bosons confined in an external harmonic potential. More precisely, we investigate the ground-state correlation properties of the system, paying particular attention to the strong-interaction limit. We explain for the first time the nature of the degeneracies appearing in this limit in the spectrum of the reduced density matrix. An explicit representation of the asymptotic natural orbitals and their occupancies is given in terms of some integral equations.Comment: 6 pages, 4 figures, To appear in European Physical Journal

Short-time-evolved wave functions for solving quantum many-body problems

The exact ground state of a strongly interacting quantum many-body system can be obtained by evolving a trial state with finite overlap with the ground state to infinite imaginary time. In many cases, since the convergence is exponential, the system converges essentially to the exact ground state in a relatively short time. Thus a short-time evolved wave function can be an excellent approximation to the exact ground state. Such a short-time-evolved wave function can be obtained by factorizing, or splitting, the evolution operator to high order. However, for the imaginary time Schrödinger equation, which contains an irreversible diffusion kernel, all coefficients, or time steps, must be positive. (Negative time steps would require evolving the diffusion process backward in time, which is impossible.) Heretofore, only second-order factorization schemes can have all positive coefficients, but without further iterations, these cannot be used to evolve the system long enough to be close to the exact ground state. In this work, we use a newly discovered fourth-order positive factorization scheme which requires knowing both the potential and its gradient. We show that the resulting fourth-order wave function alone, without further iterations, gives an excellent description of strongly interacting quantum systems such as liquid 4He, comparable to the best variational results in the literature. This suggests that such a fourth-order wave function can be used to study the ground state of diverse quantum many-body systems, including Bose-Einstein condensates and Fermi systems. © 2003 The American Physical Society