A conformal field theory description of magnetic flux  fractionalization in
Josephson junction ladders

Cristofano, Gerardo; Marotta, Vincenzo; Naddeo, Adele; Niccoli, Giuliano

doi:10.1140/epjb/e2006-00028-x

Cited by 16 publications

(38 citation statements)

References 44 publications

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“…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.…”

Section: Conclusion and Outlooksmentioning

confidence: 99%

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

Iacomino

Marotta

Naddeo

2012

Int. J. Mod. Phys. A

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In a recent paper, by exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter θ (in appropriate units), a general one-to-one correspondence between the m-reduced conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings ν = m pm+2[1, 2] and an Abelian noncommutative field theory (NCFT) has been established [3]. That allowed us to add new evidence to the relationship between noncommutativity and quantum Hall fluids [4]. On the other hand, the m-reduced CFT is equivalent to a system of two massless scalar bosons with a magnetic boundary interaction as introduced in [5], at the so called "magic" points. We are then able to describe, within such a framework, the dissipative quantum mechanics of a particle confined to a plane and subject to an external magnetic field normal to it. Here we develop such a point of view by focusing on the case m = 2 which corresponds to a quantum Hall bilayer. The key role of a localized impurity which couples the two layers is emphasized and the effect of noncommutativity in terms of generalized magnetic translations (GMT) is fully exploited. As a result, general GMT operators are introduced, in the form of a tensor product, which act on the QHF and defect space respectively, and a comprehensive study of their rich structure is performed.

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Section: Conclusion and Outlooksmentioning

confidence: 99%

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

Iacomino

Marotta

Naddeo

2012

Int. J. Mod. Phys. A

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“…Such a feature can be viewed as the localization of a topological defect which carries an elementary quantum of current, in full analogy with the half flux quantum associated with the topological defect in the closed Josephson junction ladder with MBC investigated in Refs. [27,28,29]: in this way the condition of zero total spin current in the ladder would be recovered. In presence of the railroad interaction we obtain more drastic effects, indeed the MBC turn locally on the M + 1 ≡ 1 site the interaction into a zigzag one.…”

Section: -Leg Xxz Spin-1/ladders With Mobius Boundary Conditions: Thmentioning

confidence: 99%

“…As a result of the 2-reduction procedure we obtain a c = 2 theory of two boson fields, Eqs. (28) and (29), which describe the spin chains of the two legs. Such a daughter theory is an orbifold one, which decomposes into a tensor product of two CFTs, a twisted invariant one with c = 3/2, realized by the boson X (z,z) and a Ramond Majorana fermion, while the second one has c = 1/2 and is realized in terms of a Neveu-Schwarz Majorana fermion.…”

Section: -Leg Xxz Spin-1/2 Ladders With Mobius Boundary Conditions: mentioning

confidence: 99%

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

Cristofano¹,

Marotta²,

Naddeo

et al. 2008

J. Stat. Mech.

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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.

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“…Based on the above considerations it could be possible to implement a protected qubit [9,15] with fully frustrated Josephson ladders arranged in a non trivial geometry [6].…”

Section: Josephson Junction Arrays and Ladders: A Phenomenological Dementioning

confidence: 99%

Using a hybrid CA based model for a flexible qualitative qubit simulation: fully frustrated josephson junction ladder (JJL) application

Calidonna

Naddeo²

2005

Proceedings of the 2nd Conference on Computing Frontiers

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Quantum Systems modelling and simulation activity is a challenging research area. Several models and applications were proposed in the past with different approaches. In this paper we propose a flexible qualitative model, according to the Cellular Automata Network Model version 2 (CAN2), a hybrid CA based model, for simulating a qubit. The underlying physical model is a fully frustrated JJL. Once basic system components have been individuated a core model, of the JJL device, is obtained. We show that the core model, according to different tunnelling paths, presents the same components in terms of CAN2 model. For each path different transition functions are defined. The equivalence between two different tunnelling paths shows the flexibility of the adopted scheme.

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A conformal field theory description of magnetic flux fractionalization in Josephson junction ladders

Cited by 16 publications

References 44 publications

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

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

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

Using a hybrid CA based model for a flexible qualitative qubit simulation: fully frustrated josephson junction ladder (JJL) application

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