534 research outputs found
Hartree-Fock based diagonalization: an efficient method for simulating disordered interacting electrons
We present an efficient numerical method for simulating the low-energy
properties of disordered many-particle systems. The method which is based on
the quantum-chemical configuration interaction approach consists in
diagonalizing the Hamiltonian in an energetically truncated basis build of the
low-energy states of the corresponding Hartree-Fock Hamiltonian. As an example
we investigate the quantum Coulomb glass, a model of spinless electrons in a
random potential interacting via long-range Coulomb interaction. We find that
the Coulomb interaction increases the conductance of strongly disordered
systems but reduces the conductance of weakly disordered systems.Comment: 7 pages, 3 eps figures included, invited talk at Conference on
Computational Physics (Granada, Sep 1998
Topological Conjugacies Between Cellular Automata
We study cellular automata as discrete dynamical systems and in particular investigate under which conditions two cellular automata are topologically conjugate.
Based on work of McKinsey, Tarski, Pierce and Head we introduce derivative algebras to study the topological structure of sofic shifts in dimension one. This allows us to classify periodic cellular automata on sofic shifts up to topological conjugacy based on the structure of their periodic points. We also get new conjugacy invariants in the general case. Based on a construction by Hanf and Halmos, we construct a pair of non-homeomorphic subshifts whose disjoint sums with themselves are homeomorphic. From this we can construct two cellular automata on homeomorphic state spaces for which all points have minimal period two, which are, however, not topologically conjugate. We apply our methods to classify the 256 elementary cellular automata with radius one over the binary alphabet up to topological conjugacy. By means of linear algebra over the field with two elements and identities between Fibonacci-polynomials we show that every conjugacy between rule 90 and rule 150 cannot have only a finite number of local rules. Finally, we look at the sequences of finite dynamical systems obtained by restricting cellular automata to spatially periodic points. If these sequences are termwise conjugate, we call the cellular automata conjugate on all tori. We then study the invariants under this notion of isomorphism. By means of an appropriately defined entropy, we can show that surjectivity is such an invariant
Transport in disordered interacting systems: Numerical results for one-dimensional spinless electrons
The combined influence of disorder and interactions on the transport
properties of electrons in one dimension is investigated. The numerical
simulations are carried out by means of the Hartree-Fock-based diagonalization
(HFD), a very efficient method to determine the low-energy properties of a
disordered many-particle system. We find that the conductance of a strongly
localized system can become considerably enhanced by the interactions. The
enhancement for long-range interactions is significantly larger than for
short-range interactions. In contrast, the conductance of weakly localized
systems becomes suppressed by the interactions.Comment: Invited talk presented at Percolation 98, submitted to Physica A, 8
pages, elsart style, 4 eps figures include
Fock space localization, return probability, and conductance of disordered interacting electrons
We numerically simulate the low-energy properties of interacting electrons in
a random potential using the Hartree-Fock based exact diagonalization method.
In particular, we investigate how the transport properties are influenced by
the combined effects of disorder and correlations in the presence of the
electron spin. To this end we calculate the participation number of
many-particle states in Fock space, the return probability of single-particle
excitations, and the Kubo-Greenwood conductance. It turns out that in the
strongly localized regime interactions increase the conductance whereas for
weak disorder interactions decrease the conductance. In contrast,
single-particle excitations in general experience a localizing influence of the
interactions.Comment: 4 pages, 4 eps figures, Proc. of the Symposium on Wave Propagation
and Electronic Structure in Disordered Systems, FORTH, Heraklion, Crete,
Greece (June 2000
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