Exact ground state of the generalized three-dimensional Shastry-Sutherland model

We generalize the Shastry-Sutherland model to three dimensions. By representing the model as a sum of the semidefinite positive projection operators, we exactly prove that the model has exact dimer ground state. Several schemes for constructing the three-dimensional Shastry-Sutherland model are proposed.Comment: Latex, 3 pages, 5 eps figure

Quantum to classical crossover in the 2D easy-plane XXZ model

Ground-state and thermodynamical properties of the spin-1/2 two-dimensional easy-plane XXZ model are investigated by both a Green's-function approach and by Lanczos diagonalizations on lattices with up to 36 sites. We calculate the spatial and temperature dependences of various spin correlation functions, as well as the wave-vector dependence of the spin susceptibility for all anisotropy parameters $\Delta$. In the easy--plane ferromagnetic region $(-1< \Delta < 0)$, the longitudinal correlators of spins at distance $r$ change sign at a finite temperature $T_0(\Delta, {\bf r})$. This transition, observed in the 2D case for the first time, can be interpreted as a quantum to classical crossover.Comment: 4 pages, 6 figures, Contribution to the Ising Centennial Colloquium, ICM2000, Belo Horizonte, Brazil, August 200

On the stability of polaronic superlattices in strongly coupled electron-phonon systems

We investigate the interplay of electron-phonon (EP) coupling and strong electronic correlations in the frame of the two-dimensional (2D) Holstein t-J model (HtJM), focusing on polaronic ordering phenomena for the quarter-filled band case. The use of direct Lanczos diagonalization on finite lattices allows us to include the effects of quantum phonon fluctuations in the calculation of spin/charge structure factors and hole-phonon correlation functions. In the adiabatic strong coupling regime we found evidence for ``self-localization'' of polaronic carriers in a $(\pi,\pi)$ charge-modulated structure, a type of superlattice solidification reminiscent of those observed in the nickel perovskites $La_{2-x}Sr_{x}NiO_{4+y}$.Comment: 2 pages, Latex. Submitted to Physica C, Proc. Int. Conf. on M2HTSC

A novel sampling theorem on the rotation group

We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O(L^6)$. For the common case of a low directional band-limit $N$, complexity is reduced to $O(N L^3)$. Our fast algorithms will be of direct use in speeding up the computation of directional wavelet transforms on the sphere. We make our SO3 code implementing these algorithms publicly available.Comment: 5 pages, 2 figures, minor changes to match version accepted for publication. Code available at http://www.sothree.or

Theory of short-range magnetic order for the t-J model

We present a self-consistent theory of magnetic short-range order based on a spin-rotation-invariant slave-boson representation of the 2D t-J model. In the functional-integral scheme, at the nearest-neighbour pair-approximation level, the bosonized t-J Lagrangian is transformed to a classical Heisenberg model with an effective (doping-dependent) exchange interaction which takes into account the interrelation of ``itinerant'' and ``localized'' magnetic behaviour. Evaluating the theory in the saddle-point approximation, we find a suppression of antiferromagnetic and incommensurate spiral long-range-ordered phases in the favour of a paramagnetic phase with pronounced antiferromagnetic short-range correlations.Comment: 2 pages, 1 Postscript figure, LTpaper.sty, Proc. XXI Int. Conf. on Low Temp. Phys. Prague 9

Entanglement measurement with discrete multiple coin quantum walks

Within a special multi-coin quantum walk scheme we analyze the effect of the entanglement of the initial coin state. For states with a special entanglement structure it is shown that this entanglement can be meausured with the mean value of the walk, which depends on the i-concurrence of the initial coin state. Further on the entanglement evolution is investigated and it is shown that the symmetry of the probability distribution is reflected by the symmetry of the entanglement distribution.Comment: 9 pages, IOP styl

Polaronic effects in strongly coupled electron-phonon systems: Exact diagonalization results for the 2D Holstein t-J model

Ground-state and dynamical properties of the 2D Holstein t-J model are examined by means of direct Lanczos diagonalization, using a truncation method of the phononic Hilbert space. The single-hole spectral function shows the formation of a narrow hole-polaron band as the electron-phonon coupling increases, where the polaronic band collapse is favoured by strong Coulomb correlations. In the two-hole sector, the hole-hole correlations unambiguously indicate the existence of inter-site bipolaronic states. At quarter-filling, a polaronic superlattice is formed in the adiabatic strong-coupling regime.Comment: 3 pages, LaTeX, 6 Postscript figures, Proc. Int. Conf. on Strongly Correlated Electron Systems, Zuerich, August 1996, accepted for publication in Physica