28,841 research outputs found
Quantum phase transition in the Plaquette lattice with anisotropic spin exchange
I study the influence of anisotropic spin exchange on a quantum phase
transition in the Plaquette lattice driven by the purely quantum effect of
singlet formation. I study the influence of i) a Dzyaloshinskii-Moriya exchange
and ii) four spin exchange on the transition point by evaluating spin--spin
correlations and the spin gap with exact diagonalization. The results point to
a stabilization of the Neel-like long range order when the
Dzyaloshinskii-Moriya exchange is added, whereas the four-spin exchange might
stabilize the singlet order as well as the Neel-like order depending on its
strength.Comment: LaTeX article with 4 pages and 3 figures, prepared with material for
the ICM 200
On Generalizing Decidable Standard Prefix Classes of First-Order Logic
Recently, the separated fragment (SF) of first-order logic has been
introduced. Its defining principle is that universally and existentially
quantified variables may not occur together in atoms. SF properly generalizes
both the Bernays-Sch\"onfinkel-Ramsey (BSR) fragment and the relational monadic
fragment. In this paper the restrictions on variable occurrences in SF
sentences are relaxed such that universally and existentially quantified
variables may occur together in the same atom under certain conditions. Still,
satisfiability can be decided. This result is established in two ways: firstly,
by an effective equivalence-preserving translation into the BSR fragment, and,
secondly, by a model-theoretic argument.
Slight modifications to the described concepts facilitate the definition of
other decidable classes of first-order sentences. The paper presents a second
fragment which is novel, has a decidable satisfiability problem, and properly
contains the Ackermann fragment and---once more---the relational monadic
fragment. The definition is again characterized by restrictions on the
occurrences of variables in atoms. More precisely, after certain
transformations, Skolemization yields only unary functions and constants, and
every atom contains at most one universally quantified variable. An effective
satisfiability-preserving translation into the monadic fragment is devised and
employed to prove decidability of the associated satisfiability problem.Comment: 34 page
Chern character for totally disconnected groups
In this paper we construct a bivariant Chern character for the equivariant -theory
of a totally disconnected group with values in bivariant equivariant cohomology in the sense of
Baum and Schneider. We prove in particular that the complexified left hand side of the Baum-Connes
conjecture for a totally disconnected group is isomorphic to cosheaf homology.
Moreover, it is shown that our transformation extends the Chern character defined by Baum and
Schneider for profinite groups
Equivariant local cyclic homology and the equivariant Chern-Connes character
We define and study equivariant analytic and local cyclic homology for smooth
actions of totally disconnected groups on bornological algebras. Our approach
contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki
and Lesniewski as a special case and provides an equivariant extension of the
local cyclic theory developped by Puschnigg. As a main result we construct a
multiplicative Chern-Connes character for equivariant KK-theory with values in
equivariant local cyclic homology.Comment: 38 page
On the structure of quantum automorphism groups
We compute the K-theory of quantum automorphism groups of finite dimensional C∗-algebras in the sense of Wang. The results show in particular that the C∗-algebras of functions on the quantum permutation groups S+n are pairwise non-isomorphic for different values of n. Along the way we discuss some general facts regarding torsion in discrete quantum groups. In fact, the duals of quantum automorphism groups are the most basic examples of discrete quantum groups exhibiting genuine quantum torsion phenomena
- …