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ABSTRACT: shown to develop the phenomenon of flux fractionalization [G. Cristofano, V. Marotta, A. Naddeo, G. Niccoli, Eur. Phys. J. B 49 (2006) 83]. That led us to predict the emergence of a topological order in such a system [G. Cristofano, V. Marotta, A. Naddeo, J. Stat. Mech.: Theory Exp. (2005) P03006]. In this Letter we analyze the ground states and the topological properties of fully frustrated Josephson junction arrays (JJA) arranged in a Corbino disk geometry for a variety of boundary conditions. In particular minimal configurations of fully frustrated JJA are considered and shown to exhibit the properties needed in order to build up a solid state qubit, protected from decoherence. The stability and transformation properties of the ground states of the JJA under adiabatic magnetic flux changes are analyzed in detail in order to provide a tool for the manipulation of the proposed qubit.
Physics Letters A 01/2008; 372(641):6965-6974. · 1.63 Impact Factor
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ABSTRACT: 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. 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.
Physics Letters A 01/2008; 372(74):2464-2473. · 1.63 Impact Factor
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ABSTRACT: We show how the low energy properties of the two-leg XXZ spin-1/2 ladders with general anisotropy parameter Δ on closed geometries can be accounted for in the framework of the m-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 641 547; Cristofano et al 2004 J. High Energy Phys. JHEP06(2004) 056). 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 two-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.
Journal of Statistical Mechanics Theory and Experiment 01/2008; · 1.73 Impact Factor
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ABSTRACT: Following a suggestion given in Phys. Lett. B 571(2003) 621, we show how a bilayer Quantum Hall system at fillings nu =1/p+1 can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings (Phys. Rev. B 72 (2005) 041305) which evidence the presence of a topological defect in the transport properties of the bilayer system. Comment: 10 pages, 4 figures; talk given by A. Naddeo at "X Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors, Vietri sul Mare (SA),Italy, 3-14 October 2005
06/2006;
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ABSTRACT: The composite operator T\bar{T}, obtained from the components of the energy-momentum tensor, enjoys a quite general characterization in two-dimensional quantum field theory also away from criticality. We use the form factor bootstrap supplemented by asymptotic conditions to determine its matrix elements in the sinh-Gordon model. The results extend to the breather sector of the sine-Gordon model and to the minimal models M_{2/(2N+3)} perturbed by the operator phi_{1,3}. Comment: 29 pages
02/2006;
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ABSTRACT: Following a suggestion given in Cristofano et al (2003 Phys. Lett. B 571 250; 2004 Nucl. Phys. B 679 621), we show how a bilayer quantum Hall system at fillings ν = m/(pm + 2) can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings of Deviatov et al (2005 Phys. Rev. B 72 041305) which evidence the presence of a topological defect in the bilayer system.
Journal of Statistical Mechanics Theory and Experiment 01/2006; · 1.73 Impact Factor
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ABSTRACT: Following an earlier suggestion, we show how the U (1) ⊗ Z 2 symmetry of the fully frustrated XY (F F XY) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at 'paired states' fillings ν = 1. The resulting twisted conformal field theory (CFT) with central charge c = 2 is shown to well describe the physical properties of the F F XY model. In particular, the whole phase diagram is recovered by analysing the flow from the Z 2 degenerate vacuum of the c = 2 CFT to the infrared fixed point unique vacuum of the c = 3 2 CFT. The last theory is known to successfully describe the critical behaviour of the system at the overlap temperature for the Ising and vortex-unbinding transitions.
Journal of Statistical Mechanics Theory and Experiment 01/2006; · 1.73 Impact Factor
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ABSTRACT: We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions (see cond-mat/0503555; we show how such a system can develop topological order thanks to flux fractionalization. Such a property is crucial for its implementation as a "protected" solid state qubit.
08/2005;
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ABSTRACT: We review the main results of the effective description of the Quantum Hall fluid for the Jain fillings, nu=m/2pm+1, and the non-standard ones nu=m/pm+2 by a conformal field theory (CFT) in two dimensions. It is stressed the unifying character of the m-reduction procedure to construct appropriate twisted CFT models, called Twisted Models (TM), which by construction reproduce the Quantum Hall topological properties at those fillings. Indeed for the Jain plateaux we find that the different descriptions given in the literature fall into different sectors of the TM for the torus topology. Other interesting aspects are explicitly seen for the m=2 non standard filling nu=1/p+1 (the pairing case) as the merging of non-Abelian statistics or the instability of the TM model (c=2) versus the Moore-Read one (c=3/2). Furthermore by using Boundary CFT techniques the presence of localized impurities and/or dissipation is shown to be closely connected with the twisted sector of the TM, whose presence assures the consistency of the construction and whose role in describing non trivial global properties of 2D quantum condensed matter systems is still under study.
08/2005;
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ABSTRACT: The form factors of the descendant operators in the massive Lee-Yang model
are determined up to level 7. This is first done by exploiting the conserved
quantities of the integrable theory to generate the solutions for the
descendants starting from the lowest non-trivial solutions in each operator
family. We then show that the operator space generated in this way, which is
isomorphic to the conformal one, coincides, level by level, with that implied
by the $S$-matrix through the form factor bootstrap. The solutions we determine
satisfy asymptotic conditions carrying the information about the level that we
conjecture to hold for all the operators of the model.
01/2005;
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ABSTRACT: We found new identities among the Dedekind eta-function, the characters of the W_{m} algebra and those of the level 1 affine Lie algebra su(m)_{1}. They allow to characterize the Z_{m}-orbifold of the m-component free bosons u(1)_{K_{m,p}} (our theory TM) as an extension of the fully degenerate representations of W_{1+infty}^{(m)}. In particular, TM is proven to be a Gamma _{theta}-RCFT extension of the chiral fully degenerate W_{1+infty}^{(m)}. Comment: 37 pages, minor revisions, one definition added, no formula or result has been modified
12/2004;
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ABSTRACT: Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T\bar{T} constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if the theory is integrable the addition of a requirement of factorization at high energies can lead to the exact determination of the generic matrix element of this operator on the asymptotic states. The construction is performed explicitly in the Lee-Yang model. Comment: 22 pages, one reference added
07/2004;
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ABSTRACT: We analyze the modular properties of the effective CFT description for Jain plateaux corresponding to the fillings nu=m/(2pm+1). We construct its characters for the twisted and the untwisted sector and the diagonal partition function. We show that the degrees of freedom entering the partition function go to complete a Z_{m}-orbifold construction of the RCFT U(1)xSU(m)$ proposed for the Jain states. The resulting extended algebra of the chiral primary fields can be also viewed as a RCFT extension of the U(1)xW(m) minimal models. For m=2 we prove that our model, the TM, gives the RCFT closure of the extended minimal models U(1)xW(2). Comment: 27 pages, Latex, JHEP style, no figures
06/2004;
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ABSTRACT: We analyze the modular properties of the effective CFT description for paired states, proposed in G. Cristofano, G. Maiella, V. Marrota, Mod. Phys. Lett. A 15 (2000) 1679, corresponding to the non-standard filling . We construct its characters for the twisted and the untwisted sector and the diagonal partition function. We show that the degrees of freedom entering our partition function naturally go to complete a Z2-orbifold construction of the CFT for the Halperin state. Different behaviours for the p even and p odd cases are also studied. Finally it is shown that the tunneling phenomenon selects out a twist invariant CFT which is identified with the Moore–Read model.
Nuclear Physics B. 04/2002;
