Bosonization and effective vector-field theory of the fractional quantum Hall effect

Shizuya, K.

doi:10.1103/physrevb.63.245301

Cited by 6 publications

(7 citation statements)

References 30 publications

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“…This approach naturally is only meaningful for massive theories. In the case of massive Dirac fermions in D = 2 + 1 dimensions it has been shown [51][52][53][54][55][56] that the correlation functions of the conserved fermionic currents are the same as the correlation functions of a dual topological Chern-Simons gauge theory in the low energy regime (only!). A mapping of the correlators of other fermion bilinears can also be determined but, again, only in the low-energy and long wavelength regime.…”

Section: B Generalitiesmentioning

confidence: 99%

Effective field theories for topological insulators by functional bosonization

et al. 2013

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Effective field theories that describes the dynamics of a conserved U(1) current in terms of "hydrodynamic" degrees of freedom of topological phases in condensed matter are discussed in general dimension D = d+1 using the functional bosonization technique. For non-interacting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII) and in the "primary series" of topological insulators in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when D is odd) or the θ-term (when D is even). For topological insulators characterized by a Z2 topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative "fractional" topological insulators and their possible effective field theories, and use them to determine the physical properties of these non-trivial quantum phases.

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Section: B Generalitiesmentioning

confidence: 99%

Effective field theories for topological insulators by functional bosonization

et al. 2013

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“…It readily admits inclusion of vortices, and is thus applicable to the description of the fractional QH effect as well. It furthermore unifies 25 the compositeboson 26 and composite-fermion 27 descriptions of the fractional QH effect.…”

Section: Long-wavelength Effective Theorymentioning

confidence: 88%

Electromagnetic response and effective gauge theory of graphene in a magnetic field

Shizuya

2007

Phys. Rev. B

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The electromagnetic response of graphene in a magnetic field is studied, with particular emphasis on the quantum features of its ground state (vacuum). The graphene vacuum, unlike in conventional quantum Hall systems, is a dielectric medium and carries an appreciable amount of electric and magnetic susceptibilities. The dielectric effect grows rapidly with increasing filling factor ν in such a way that reflects the 'relativistic' Landau-level characteristics of graphene as well as its valley and spin degeneracy. A close look into the dielectric function also reveals that the Coulomb interaction is efficiently screened on the scale of the magnetic length, leading to a prominent reduction of the exciton spectra in graphene. In addition, an effective gauge theory of graphene is constructed out of the response. It is pointed out thereby that the electric susceptibility is generally expressed as a ratio of the Hall conductance to the Landau gap.

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“…Once such a response is known, it is possible to reconstruct it through the quantum fluctuations of a boson field. This procedure, known as functional bosonization, 29 was previously applied to single-layer systems to derive 11 an effective theory of the FQHE. In this section we construct an effective theory for the double-layer system.…”

Section: Effective Gauge Theorymentioning

confidence: 99%

“…An alternative approach, 11 that makes use of projection to Landau levels and bosonization as basic tools, has recently been developed to study the long-wavelength features of single-layer quantum Hall systems. There an effective vector-field theory is constructed, via bosonization, from the electromagnetic response of incompressible states.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic characteristics and effective gauge theory of double-layer quantum Hall systems

Shizuya

2002

Phys. Rev. B

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The electromagnetic characteristics of double-layer quantum Hall systems are studied, with projection to the lowest Landau level taken into account and intra-Landau-level collective excitations treated in the single-mode approximation. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems. In particular, the presence of the dipoleactive interlayer out-of-phase collective excitations, inherent to double-layer systems, modifies the leading O(k) and O(k 2 ) long-wavelength characteristics (i.e., the transport properties and characteristic scale) of the double-layer quantum Hall states substantially. We apply bosonization techniques and construct from such electromagnetic characteristics an effective theory, which consists of three vector fields representing the three dipole-active modes, one interlayer collective mode and two inter-Landau-level cyclotron modes. This effective theory properly incorporates the spectrum of collective excitations on the right scale of the Coulomb energy and, in addition, accommodates the favorable transport properties of the standard Chern-Simons theories.73.43.Lp, 73.21.Ac

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Bosonization and effective vector-field theory of the fractional quantum Hall effect

Cited by 6 publications

References 30 publications

Effective field theories for topological insulators by functional bosonization

Effective field theories for topological insulators by functional bosonization

Electromagnetic response and effective gauge theory of graphene in a magnetic field

Electromagnetic characteristics and effective gauge theory of double-layer quantum Hall systems

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