Showing papers by "Andreas Schadschneider published in 1995"
TL;DR: This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models and calculates the so-called fundamental diagrams (flow vs. density) for parallel dynamics by means of an improved mean-field approximation.
Abstract: We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow versus density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with a maximum velocity of 1, the simplest nontrivial approximation gives the exact result. For higher velocities, the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.
420 citations
TL;DR: It is shown that a large class of extended versions of the Hubbard model has a superconducting ground state in arbitrary dimensions and in some special cases the complete phase diagram is found.
Abstract: We consider extended versions of the Hubbard model which contain additional interactions between nearest neighbors. In this Letter we show that a large class of these models has a superconducting ground state in arbitrary dimensions. In some special cases we are able to find the complete phase diagram. The superconducting phase exists even for moderate repulsive values of the Hubbard interaction $U$.
103 citations
TL;DR: This method is used to derive rigorous criteria for the stability of various ground state types, like the $\eta$-pairing state, or N\'eel and ferromagnetic states, and yields better bounds for the region of stability.
Abstract: We present a simple method for the construction of exact ground states of generalized Hubbard models in arbitrary dimensions. This method is used to derive rigorous criteria for the stability of various ground state types, like the $\eta$-pairing state, or N\'eel and ferromagnetic states. Although the approach presented here is much simpler than the ones commonly used, it yields better bounds for the region of stability.
62 citations
TL;DR: It is shown that for moderate Hubbard interactions {ital U} the model has superconducting ground states and the qualitative form of the phase diagram is obtained.
Abstract: The Hubbard model with an additional bond-charge interaction X is solved exactly in one dimension for the case t=X, where t is the hopping amplitude. In this case the number of doubly occupied sites is conserved. In the sector with no double occupations the model reduces to the U=\ensuremath{\infty} Hubbard model. In arbitrary dimensions the qualitative form of the phase diagram is obtained. It is shown that for moderate Hubbard interactions U the model has superconducting ground states.
58 citations
TL;DR: In this paper, a generalization of the supersymmetrict−J model in one dimension is investigated and the critical behavior is described by ac=1 conformal field theory with continuously varying exponents depending on the particle density.
Abstract: A recently presented anisotropic generalization of the multicomponent supersymmetrict−J model in one dimension is investigated. This model of fermions with general spin-S is solved by Bethe ansatz for the ground state and the low-lying excitations. Due to the anisotropy of the interaction the model possesses 2S massive modes and one single gapless excitation. The physical properties indicate the existence of Cooper-type multiplets of 2S+1 fermions with finite binding energy. The critical behaviour is described by ac=1 conformal field theory with continuously varying exponents depending on the particle density. There are two distinct regimes of the phase diagram with dominating density-density and multiplet-multiplet correlations, respectively. The effective mass of the charge carriers is calculated. In comparison to the limit of isotropic interactions the mass is strongly enhanced in general.
21 citations
TL;DR: In this article, the authors studied the phase diagram of the bilinear-biquadratic spin-1 chain and obtained upper bounds for the groundstate energy using so-called matrix-product states.
Abstract: We study the phase diagram of the bilinear-biquadratic spin-1 chain. Using so-called matrix-product (MP) states we obtain upper bounds for the groundstate energy. The advantage of these MP states is their simplicity. Moreover they give an accurate description of the physics, especially in the Haldane phase.
17 citations
TL;DR: In this paper, a model with both single-particle and multiparticle hopping of electrons on a one-dimensional "triangular" lattice is formulated and solved exactly by Bethe ansatz.
Abstract: A model with both single-particle and multi-particle hopping of electrons on a one-dimensional 'triangular' lattice is formulated and solved exactly by Bethe ansatz. On the basis of the exact calculation of the asymptotic behaviour of correlation functions we find a transition between the normal state and a state with a tendency to 'superconductivity'. The latter state is confined to small densities of electrons up to a critical density rho c.
12 citations
TL;DR: In this article, the ground-state properties of two correlated-hopping electron models are compared for small-chain systems and it is shown that pairing is preferred in a certain parameter range.
Abstract: We compare ground-state properties of two correlated-hopping electron models. The Hirsch model has been of recent interest in the context of hole superconductivity. A modified version of this model, the Bariev model, is exactly solvable by Bethe ansatz in one dimension. Applying the Lanczos technique to small chains, we numerically determine the binding energy, the spin gaps, correlation functions, and other properties for various values of the bond-charge interaction parameter. Our results for small systems indicate that pairing is favoured in a certain parameter range. However, in contrast to the Bariev model, superconducting correlations are suppressed in the Hirsch model, for a bond-charge repulsion larger than a critical value. Below that critical value the two models exhibit similar physical behaviour.
4 citations
TL;DR: In this paper, the ground-state properties of two correlated-hopping electron models, the Hirsch and the Bariev model, were investigated in the context of hole superconductivity.
Abstract: We investigate ground-state properties of two correlated-hopping electron models, the Hirsch and the Bariev model. Both models are of recent interest in the context of hole superconductivity. Applying the Lanczos technique to small clusters, we numerically determine the binding energy, the spin gaps, correlation functions, and other properties for various values of the bond-charge interaction parameter. Our results for small systems indicate that pairing is favoured in a certain parameter range. However, in contrast to the Bariev model, superconducting correlations are suppressed in the Hirsch model, for a bond-charge repulsion larger than a critical value.
3 citations
01 Jan 1995
TL;DR: In this paper, the authors provide rigourous results on the behaviour of correlated electrons in the presence of strong quantum fluctuations and thus may give some guidance at how to interpret observations in the much less well understood models in higher dimensions.
Abstract: Studies of exactly soluble models for correlated electrons in one dimension have attracted wide spread interest in recent years. The reason for this is simple: they provide rigourous results on the behaviour of these systems in the presence of strong quantum fluctuations and thus may give some guidance at how to interpret observations in the much less well understood models in higher dimensions.
3 citations
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TL;DR: A modified cellular automaton is presented which is closely related to a two-dimensional dimer model and goes beyond mean-field using the so-called $n$-cluster approach, in excellent agreement with numerical simulations.
Abstract: We use analytical methods to investigate cellular automata for traffic flow. Two different mean-field approaches are presented, which we call site-oriented and car-oriented, respectively. The car-oriented mean-field theory yields the exact fundamental diagram for the model with maximum velocity $\vm =1$ whereas in the site-oriented approach one has to take into account correlations between nearest-neighbour sites. Going beyond mean-field using the so-called $n$-cluster approach our results for $\vm >1$ are in excellent agreement with numerical simulations. We also present a modified cellular automaton which is closely related to a two-dimensional dimer model.
TL;DR: In this paper, the authors propose a bridge between the theory of exactly solvable models and the investigation of traffic flow, by choosing the activities in an apropriate way the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as space-time trajectories of cars.
Abstract: We propose a bridge between the theory of exactly solvable models and the investigation of traffic flow. By choosing the activities in an apropriate way the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as space-time trajectories of cars. This then allows for a calculation of the flow-density relationship (fundamental diagram). We further introduce a closely-related cellular automaton model. This model can be viewed as a variant of the Nagel-Schreckenberg model in which the cars do not have a velocity memory. It is also exactly solvable and the fundamental diagram is calculated.