5 research outputs found
Competing effects of interactions and spin-orbit coupling in a quantum wire
We study the interplay of electron-electron interactions and Rashba
spin-orbit coupling in one-dimensional ballistic wires. Using the
renormalization group approach we construct the phase diagram in terms of
Rashba coupling, Tomonaga-Luttinger stiffness and backward scattering strength.
We identify the parameter regimes with a dynamically generated spin gap and
show where the Luttinger liquid prevails. We also discuss the consequences for
the operation of the Datta-Das transistor.Comment: 4 pages, 2 figure
Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange
We investigate the phase diagram of a generalized spin-1/2 quantum
antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange
interactions. We consider the exactly soluble models associated with the
problem, obtain the exact ground states which exist for certain parameter
regimes, and apply a variety of perturbative techniques in the regime of strong
ring-exchange coupling. By combining these approaches with considerations
related to the discrete Z_4 symmetry of the model, we present the complete
phase diagram.Comment: 17 pages, 10 figure
The bubble algebra: structure of a two-colour Temperley–Lieb Algebra
We define new diagram algebras providing a sequence of multiparameter generalizations of the Temperley–Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional statistical mechanics. These algebras give a rigorous foundation to the various 'multi-colour algebras' of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in statistical mechanics. We demonstrate how these algebras may be used to solve the Yang–Baxter equations