A general CFT model for antiferromagnetic spin-1/2 ladders with Mobius boundary conditions

Abstract

We show how the low-energy properties of the 2-leg XXZ spin-1/2 ladders with general anisotropy parameter ∆ on closed geometries can be accounted for in the framework of the m-reduction procedure developed in [1]. In the limit of quasi-decoupled chains, a conformal field theory (CFT) with central charge c = 2 is derived and its ability to describe the model with different boundary conditions is shown. Special emphasis is given to the Mobius boundary conditions which generate a topological defect corresponding to non trivial single-spinon excitations. Then, in the case of the 2-leg XXX ladders we discuss in detail the role of various perturbations in determining the renormalization group flow starting from the ultraviolet (UV) critical point with c = 2.

Dissipative Quantum Mechanics and Kondo-Like Impurities on Noncommutative Two-Tori

“…Finally, we would stress that our work helps to shed new light on the relationship between noncommutativity and QHF physics on one hand and between string and D-brane theory and QHF physics on the other hand [35]. Recently we employed the m-reduction procedure in order to describe non trivial phenomenology in different condensed matter systems such as Josephson junction ladders and arrays [36], two-dimensional fully frustrated XY models [37] and antiferromagnetic spin-1/2 ladders with a variety of interactions [38]. The role of noncommutativity in these systems is now under study and will be the subject of future publications.…”

Paired quantum Hall states on noncommutative two-tori

“…Recently, the twisted CFT approach provided by m-reduction and developed for a QHF at paired states fillings [1] [43] has been successfully applied to Josephson junction ladders and arrays of non trivial geometry in order to investigate the existence of topological order and magnetic flux fractionalization in view of the implementation of a possible solid state qubit protected from decoherence [64,65,66] as well as to the study of the phase diagrams of the fully frustrated XY model (F F XY ) on a square lattice [67] and of a general spin-1/2 antiferromagnetic two leg ladder with Mobius boundary conditions in the presence of various perturbations [68]. So, it could be interesting to generalize our approach in order to further elucidate the topological properties of Josephson systems with non trivial geometry as well as the deep nature of the quantum critical points and of the deconfinement of excitations with fractional quantum numbers in antiferromagnetic spin ladders and the consequences imposed upon them by the request of space-time noncommutativity.…”