arXiv subjects

Walter Apel

Publications and source records attributed to Walter Apel.

4 recordsLinked to original sources

arXiv2014

Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions

We present a large-scale combinatorial-diagrammatic computation of high-order contributions to the strong-coupling Kato-Takahashi perturbation series for the Hubbard model in high dimensions. The ground-state energy of the Mott-insulating phase is determined exactly up to the 15-th order in 1/U. The perturbation expansion is extrapolated to infinite order and the critical behavior is determined using the Domb-Sykes method. We compare the perturbative results with two dynamical mean-field theory (DMFT) calculations using a quantum Monte Carlo method and a density-matrix renormalization group method as impurity solvers. The comparison demonstrates the excellent agreement and accuracy of both extrapolated strong-coupling perturbation theory and quantum Monte Carlo based DMFT, even close to the critical coupling where the Mott insulator becomes unstable.

cond-mat.str-el↗

arXiv2011

Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

We study the correlation function of middle spins, i. e. of spins on intermediate sites between two adjacent parallel lattice axes, of the spatially anisotropic Ising antiferromagnet on the kagome lattice. It is given rigorously by a Toeplitz determinant. The large-distance behaviour of this correlation function is obtained by analytic methods. For shorter distances we evaluate the Toeplitz determinant numerically. The correlation function is found to vanish exactly on a line J_d(T) in the T-J (temperature vs. coupling constant) phase diagram. This disorder line divides the phase diagram into two regions. For J less than J_d(T) the correlations display the features of an unfrustrated two-dimensional Ising magnet, whereas for J greater than J_d(T) the correlations between the middle spins are seen to be strongly influenced by the short-range antiferromagnetic order that prevails among the spins of the adjacent lattice axes. While for J less than J_d(T) there is a region with ferrimagnetic long-range order, the model remains disordered for J greater than J_d(T) down to T=0.

cond-mat.stat-mech↗

arXiv1996

Exact density of states of a two-dimensional electron gas in a strong magnetic field and a long-range correlated random potential

We derive an exact result for the averaged Feynman propagator and the corresponding density of states of an electron in two dimensions in a perpendicular homogeneous magnetic field and a Gaussian random potential with long-range spatial correlations described by a quadratic correlation function.

cond-mat.mes-hall↗

arXiv1992

A new Proposal for a Quasielectron Trial Wavefunction for the FQHE on a Disk

In this letter, we propose a new quasielectron trial wavefunction for $N$ interacting electrons in two dimensions moving in a strong magnetic field in a disk geometry. Requiring that the trial wavefunction exhibits the correct filling factor of a quasielectron wavefunction, we obtain $N+1$ angular momentum eigenfunctions. The expectation values of the energy are calculated and compared with the data of an exact numerical diagonalization.

cond-mat↗