Mobius Boundary Conditions Research Articles

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

We show how the low energy properties of the two-leg XXZspin-1/2 ladders with generalanisotropy parameter Δ on closed geometries can be accounted for in the framework of them-reduction procedure developed previously (Cristofano et al 2000 Mod. Phys. Lett. A 15 547;Cristofano et al 2000 Mod. Phys. Lett. A 15 1679; Cristofano et al 2002 Nucl. Phys. B 641547; Cristofano et al 2004 J. High Energy Phys. JHEP06(2004) 056). In the limitof quasi-decoupled chains, a conformal field theory (CFT) with central chargec = 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 topologicaldefect corresponding to non-trivial single-spinon excitations. Then, in the case of thetwo-leg XXX ladders we discuss in detail the role of various perturbations in determiningthe renormalization group flow starting from the ultraviolet (UV) critical point withc = 2.

Fully frustrated Josephson junction ladders with Mobius boundary conditions as topologically protected qubits

We show how to realize a “protected” qubit by using a fully frustrated Josephson junction ladder (JJL) with Mobius boundary conditions. Such a system has been recently studied within a twisted conformal field theory (CFT) approach [G. Cristofano, G. Maiella, V. Marotta, Mod. Phys. Lett. A 15 (2000) 1679; G. Cristofano, G. Maiella, V. Marotta, G. Niccoli, Nucl. Phys. B 641 (2002) 547] and shown to develop the phenomenon of flux fractionalization [G. Cristofano, V. Marotta, A. Naddeo, G. Niccoli, Eur. Phys. J. B 49 (2006) 83]. The relevance of a “closed” geometry has been fully exploited in relating the topological properties of the ground state of the system to the presence of half flux quanta and the emergence of a topological order has been predicted [G. Cristofano, V. Marotta, A. Naddeo, J. Stat. Mech.: Theory Exp. (2005) P03006]. In this Letter the stability and transformation properties of the ground states under adiabatic magnetic flux change are analyzed and the deep consequences on the realization of a solid state qubit, protected from decoherence, are presented.

Topological order in Josephson junction ladders with Mobius boundary conditions

We propose a CFT description for a closed one-dimensional fully frustrated ladder ofquantum Josephson junctions with Mobius boundary conditions; in particular we show howsuch a system can develop topological order. Such a property is crucial for itsimplementation as a ‘protected’ solid state qubit.