Gauge theories of Josephson junction arrays

Diamantini, M. C.; Sodano, P.; Trugenberger, Carlo A.

doi:10.1016/0550-3213(96)00309-4

Cited by 126 publications

(241 citation statements)

References 54 publications

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“…We are led to predict the above startling properties for bosonic Quantum Hall systems, such as someday might be obtained from superconductor-insulator transitions in thin films, or from Josephson-junction arrays [50][51][52][53][54]. Unfortunately, these predictions cannot yet be tested with ordinary superconductors, because charge carrier densities and mobilities in these systems do not put them into the quantum Hall regime [55].…”

Section: Universal Critical Points Are Predicted For the Flowmentioning

confidence: 99%

Particle-vortex duality and the modular group: Applications to the quantum Hall effect and other two-dimensional systems

2001

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We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers satisfying Fermi statistics (or those related to fermions by the action of the group), the resulting group is known to imply many, if not all, of the remarkable features of Quantum Hall systems. For conductors with boson charge carriers (modulo group transformations) a different group is predicted, implying equally striking implications for the conductivities of these systems, including a super-universality of the critical exponents for conductor/insulator and superconductor/insulator transitions in two dimensions and a hierarchical structure, analogous to that of the quantum Hall effect but different in its details. Our derivation shows how this symmetry emerges at low energies, depending only weakly on the details of dynamics of the underlying systems.

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Section: Universal Critical Points Are Predicted For the Flowmentioning

confidence: 99%

Particle-vortex duality and the modular group: Applications to the quantum Hall effect and other two-dimensional systems

2001

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“…It is interesting to notice that in (3.2) what lead to confinement is the condensation of the topological defects that enter the theory as a minimally coupled current and, as we explained before, are associated on the lattice with the breaking the global gauge symmetry down to Z t . A similar phase was found in [18], in the context of effective field theories for 3-dimensional Josephson junction arrays, studying a model in which the original gauge group was non-compact and only the BF coupling was periodic. Also in (3.6), as expected, the further condensation of thet µ gives a volume law for the expectation value of the Wilson "surface".…”

Section: Condensation Of Topological Defects In the 4-dimensional Casementioning

confidence: 87%

“…In this magnetic condensation phase, a lenghty calculation shows that the self energy of a circular charge loop of radius R is proportional to R ln R, and this gives rise to logarithmic confinement of electric strings (logarithmic confinement phase) [18]. The monopoles Q are always in a plasma phase : their condensation (after the condensation of t µ ), as it was shown in [10], gives a volume law and thus the usual confinement strings.…”

Section: Condensation Of Topological Defects In the 4-dimensional Casementioning

confidence: 99%

Duality and confinement in massive antisymmetric tensor gauge theories

Diamantini

2001

Physics Letters B

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We extend the duality between massive and topologically massive antisymmetric tensor gauge theories in arbitrary space-time dimensions to include topological defects. We show explicitly that the condensation of these defects leads, in 4 dimensions, to confinement of electric strings in the two dual models. The dual phase, in which magnetic strings are confined is absent. The presence of the confinement phase explicitely found in the 4-dimensional case, is generalized, using duality arguments, to arbitrary space-time dimensions.

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“…Something very interesting happens when the additional marginal terms in the effective action combine with the original ones to give (7). Suppose, moreover, that the charge current is identified with the boundaries of the now open world-surfaces of the vortices as J µ = 2∂ ν Φ µν , so that the interaction can be combined into…”

mentioning

confidence: 99%

“…Mixed Chern-Simons fluids as representations of condensed matter systems where first introduced in [7], where it was shown that they capture all the essential physics of 2D Josephson junction arrays. In the same paper it was also pointed out that this two-fluid construction can be generalized to 3D, the topological interaction being encoded in what is known as the BF term [8].…”

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confidence: 99%

Spin-charge soldering from tensor Higgs mechanism

Diamantini

Trugenberger²

2014

Phys. Rev. D

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Spin-charge separation, a crucial ingredient in 2D models of strongly correlated systems, in mostly considered in condensed matter applications. In this paper we present a relativistic field-theoretic model in which charged particles of spin 1/2 emerge by soldering spinless charges and magnetic vortices in a confinement quantum phase transition modelled as a tensor Higgs mechanism. The model involves two gauge fields, a vector one and a two-form gauge field interacting by the topological BF term. When this tensor gauge symmetry is spontaneously broken charges are soldered to the ends of magnetic vortices and thus confined by a linear potential. If the vector potential has a topological θ-term with value θ = π, the constituents of this "meson" acquire spin 1/2 in this transition.PACS numbers: 11.15.Wx,73.43.Nq The concept of spin-charge separation is one of the guiding principles of the modern approach to strongly correlated, low-dimensional systems [1]. The idea is that, in specific ground states, the electron is fractionalized into two "constituent" quasi-particles, the chargeon (holon), carrying only the charge degree of freedom and the spinon, carrying only the spin degree of freedom. The two quasi-particles interact via emergent gauge fields: the electron is reconstituted when the gauge interaction becomes strong enough to cause confinement. This mechanism was shown by Haldane [2] to be a generic feature of 1D metallic systems. Moreover, the idea of electron fractionalization is thought to play a crucial role in the physics of the high-T c cuprates. Indeed, spin-charge separation seems to be an unavoidable characteristics of the 2D tJ model [3,4] of the doped Mott insulators, capturing the essential physics of high-T c superconductivity [5]. Electron fractionalization in these models leads to new quantum orders not characterized by symmetry breaking [6].A key ingredient of the spin-charge separation idea in 2D is the representation of chargeons and spinons as a two-fluid model with mutual Chern-Simons interactions [5], a picture that can be analytically derived from the tJ model [3,4]. Mixed Chern-Simons fluids as representations of condensed matter systems where first introduced in [7], where it was shown that they capture all the essential physics of 2D Josephson junction arrays. In the same paper it was also pointed out that this two-fluid construction can be generalized to 3D, the topological interaction being encoded in what is known as the BF term [8]. Fractionalization in higher dimensions was fur- * Electronic address: cristina.diamantini@pg.infn.it † Electronic address: ca.trugenberger@bluewin.ch ther studied in [9] in the context of microscopic two-fluid lattice models.Spin-charge separation has been studied mainly in the framework of condensed matter models. Much less is known about the possibility of such fractionalisation in the context of relativistic field theory. In this paper we present a simple model in which we show that charged particles with spin 1/2 emerge in a model of spinless char...

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Gauge theories of Josephson junction arrays

Cited by 126 publications

References 54 publications

Particle-vortex duality and the modular group: Applications to the quantum Hall effect and other two-dimensional systems

Particle-vortex duality and the modular group: Applications to the quantum Hall effect and other two-dimensional systems

Duality and confinement in massive antisymmetric tensor gauge theories

Spin-charge soldering from tensor Higgs mechanism

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