Theory of the quantum Hall Smectic Phase. I. Low-energy properties of the quantum Hall smectic fixed point

Barci, Daniel G.; Fradkin, Eduardo; Kivelson, Steven A.; Oganesyan, Vadim

doi:10.1103/physrevb.65.245319

Cited by 40 publications

(77 citation statements)

References 43 publications

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“…[34,35,36,37,38,39,40]). Recent work on these interesting phases of the two-dimensional electron gas has revealed that magnetic symmetry plays a crucial role in low-energy dynamics of these states.…”

Section: Discussionmentioning

confidence: 99%

Non-commutative Chern–Simons for the quantum Hall system and duality

2002

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The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of ChernSimons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized only through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.

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Section: Discussionmentioning

confidence: 99%

Non-commutative Chern–Simons for the quantum Hall system and duality

2002

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“…[10][11][12][19][20][21] The rise of the smectic phase softens the magnetoroton mode and appears to be responsible for the reduction of the excitation gap for 2.0 < A c < 8.0 as shown in Fig. 1.…”

Section: B Hall-smectic-like Phase In the Intermediate Interaction Amentioning

confidence: 99%

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

et al. 2012

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We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hallsmectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [Phys. Rev. Lett. 107, 116801 (2011)].

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“…In our model we have concentrated on a single string and assumed that rotational invariance has been completely broken, possibly due to a strong orienting field originating from the underlying lattice. A more realistic treatment of smectic and nematic stripe phases in the cuprates should include the interactions between stripes, which are expected to be invariant under small rotations 14 . We defer the study of these issues to the future.…”

Section: Discussionmentioning

confidence: 99%

“…A notable exception is the study of the smectic phase in quantum Hall samples [14][15][16][17][18] . This theory presupposes the existence of a unidirectional charge density wave in the sample and focuses on the quantum mechanical description of the fluctuating chiral edge channels that develop on the boundaries between regions of different filling fraction.…”

Section: Introductionmentioning

confidence: 99%

“…Secondly, in addition to the existence of various quasi-one-dimensional compounds such as organic Bachgaard salts 3 and inorganic purple bronzes 4 , there is a growing set of higher dimensional systems whose experimentally observed behavior appears to be, nevertheless, quasi-one-dimensional. Among them one finds the high temperature superconductors [5][6][7][8][9] , the manganites 10 and quantum Hall systems [11][12][13][14] . It is possible that the electronic structure of these materials is actually quasi-one-dimensional on a local scale.…”

Section: Introductionmentioning

confidence: 99%

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Interacting electrons on a fluctuating string

Orgad

2004

Phys. Rev. B

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We consider the problem of interacting electrons constrained to move on a fluctuating onedimensional string. An effective low-energy theory for the electrons is derived by integrating out the string degrees of freedom to lowest order in the inverse of the string tension and mass density, which are assumed to be large. We obtain expressions for the tunneling density of states, the spectral function and the optical conductivity of the system. Possible connections with the phenomenology of the cuprate high temperature superconductors are discussed.

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Theory of the quantum Hall Smectic Phase. I. Low-energy properties of the quantum Hall smectic fixed point

Cited by 40 publications

References 43 publications

Non-commutative Chern–Simons for the quantum Hall system and duality

Non-commutative Chern–Simons for the quantum Hall system and duality

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

Interacting electrons on a fluctuating string

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