arXiv subjects

F. Wagner

Publications and source records attributed to F. Wagner.

42 records · Page 3Linked to original sources

arXiv2000

Symplectic and orthogonal Lie algebra technology for bosonic and fermionic oscillator models of integrable systems

To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper develops a presentation of these Lie algebras convenient for the context, and derives many properties of the matrices of their defining representations and of the ad-invariant tensors that enter their multiplication laws. Metaplectic-type representations of sp(2n) and so(N) on bosonic and on fermionic Fock spaces respectively are constructed. Concise general expressions (see (5.2) and (5.5) below) for their L-operators are obtained, and used to derive simple formulas for the T operators of the rational RTT algebra of the associated integral systems, thereby enabling their efficient treatment by means of the algebraic Bethe ansatz.

math-ph↗

arXiv2000

The k-folded sine-Gordon model in finite volume

We consider the k-folded sine-Gordon model, obtained from the usual version by identifying the scalar field after k periods of the cosine potential. We examine (1) the ground state energy split, (2) the lowest lying multi-particle state spectrum and (3) vacuum expectation values of local fields in finite spatial volume, combining the Truncated Conformal Space Approach, the method of the Destri-de Vega nonlinear integral equation (NLIE) and semiclassical instanton calculations. We show that the predictions of all these different methods are consistent with each other and in particular provide further support for the NLIE method in the presence of a twist parameter. It turns out that the model provides an optimal laboratory for examining instanton contributions beyond the dilute instanton gas approximation. We also provide evidence for the exact formula for the vacuum expectation values conjectured by Lukyanov and Zamolodchikov.

hep-th↗

arXiv1999

Yang-Baxter Algebra for the n-Harmonic Oscillator Realisation of sp(2n,R)

Using a rational R-matrix associated with the 4 x 4 defining matrix representation of c_2=sp(4), the Lie algebra of Sp(4), a one-site operator solution of the associated Yang-Baxter algebra acting in the Fock space of two harmonic oscillators is derived. This is used to define N-site integrable systems, which are soluble by a version of the algebraic Bethe ansatz method without nesting. All essential aspects of the work generalise directly from c_2 to c_n.

solv-int↗

arXiv1998

The hematite (alpha-Fe_2 O_3) (0001) surface: evidence for domains of distinct chemistry

Using spin-density functional theory we investigated various possible structures of the hematite (0001) surface. Depending on the ambient oxygen partial pressure, two geometries are found to be particularly stable under thermal equilibrium: one being terminated by iron and the other by oxygen. Both exhibit huge surface relaxations (-57 % for the Fe- and -79 % for the O-termination) with important consequences for the surface electronic and magnetic properties. With scanning tunneling microscopy we observe two different surface terminations coexisting on single crystalline alpha-Fe_2 O_3 (0001) films, which were prepared in high oxygen pressures.

cond-mat.mtrl-sci↗

arXiv1997

Errors in Hellmann-Feynman Forces due to occupation number broadening, and how they can be corrected

In ab initio calculations of electronic structures, total energies, and forces, it is convenient and often even necessary to employ a broadening of the occupation numbers. If done carefully, this improves the accuracy of the calculated electron densities and total energies and stabilizes the convergence of the iterative approach towards self-consistency. However, such a boardening may lead to an error in the calculation of the forces. Accurate forces are needed for an efficient geometry optimization of polyatomic systems and for ab initio molecular dynamics (MD) calculations. The relevance of this error and possible ways to correct it will be discussed in this paper. The first approach is computationally very simple and in fact exact for small MD time steps. This is demonstrated for the example of the vibration of a carbon dimer and for the relaxation of the top layer of the (111)-surfaces of aluminium and platinum. The second, more general, scheme employs linear-response theory and is applied to the calculation of the surface relaxation of Al(111). We will show that the quadratic dependence of the forces on the broadening width enables an efficient extrapolation to the correct result. Finally the results of these correction methods will be compared to the forces obtained by using the smearing scheme, which has been proposed by Methfessel and Paxton.

cond-mat.mtrl-sci↗

arXiv1994

Correlation Function in Ising Models

We simulated the fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the available exact results in $d=2$, which shows, that the cluster algorithm can succesfully be applied for correlations. We show as a further result that our data do not support a hypothesis of Fisher that in any $d=2$ lattice the fourier transform of the correlation function depends on the lattice generating function only. In $d=3$ our simulation are again in agreement with the results from the series expansion, except for the amplitudes $f_{\pm}$, where we find $f_+/f_-=2.06(1)$.

hep-lat↗