86 research outputs found

    Is the Composite Fermion a Dirac Particle?

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    We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in the magnetic field at charge neutrality, as well as for the Ξ½=12\nu=\frac12 quantum Hall ground state of nonrelativistic fermions in the limit of negligible inter-Landau-level mixing. We argue that when particle-hole symmetry is exact, the composite fermion is a massless Dirac fermion, characterized by a Berry phase of Ο€\pi around the Fermi circle. We write down a tentative effective field theory of such a fermion and discuss the discrete symmetries, in particular, CP\mathcal C\mathcal P. The Dirac composite fermions interact through a gauge, but non-Chern-Simons, interaction. The particle-hole conjugate pair of Jain-sequence states at filling factors n2n+1\frac n{2n+1} and n+12n+1\frac{n+1}{2n+1}, which in the conventional composite fermion picture corresponds to integer quantum Hall states with different filling factors, nn and n+1n+1, is now mapped to the same half-integer filling factor n+12n+\frac12 of the Dirac composite fermion. The Pfaffian and anti-Pfaffian states are interpreted as dd-wave Bardeen-Cooper-Schrieffer paired states of the Dirac fermion with orbital angular momentum of opposite signs, while ss-wave pairing would give rise to a particle-hole symmetric non-Abelian gapped phase. When particle-hole symmetry is not exact, the Dirac fermion has a CP\mathcal C\mathcal P-breaking mass. The conventional fermionic Chern-Simons theory is shown to emerge in the nonrelativistic limit of the massive theory.Comment: 13 pages; v2: added discussion of experimental signatures, Kohn's theorem; v3: typo fixed, published versio

    Hydrodynamics on the lowest Landau level

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    Using the recently developed approach to quantum Hall physics based on Newton-Cartan geometry, we consider the hydrodynamics of an interacting system on the lowest Landau level. We rephrase the non-relativistic fluid equations of motion in a manner that manifests the spacetime diffeomorphism invariance of the underlying theory. In the massless (or lowest Landau level) limit, the fluid obeys a force-free constraint which fixes the charge current. An entropy current analysis further constrains the energy response, determining four transverse response functions in terms of only two: an energy magnetization and a thermal Hall conductivity. Kubo formulas are presented for all transport coefficients and constraints from Weyl invariance derived. We also present a number of Streda-type formulas for the equilibrium response to external electric, magnetic and gravitational fields

    Bimetric Theory of Fractional Quantum Hall States

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    We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as Girvin-Macdonald-Platzman (GMP) mode. The theory consist of a topological Chern-Simons action, coupled to a symmetric rank two tensor, and an action \`a la bimetric gravity, describing the gapped dynamics of the spin-22 GMP mode. The theory is formulated in curved ambient space and is spatially covariant, which allows to restrict the form of the effective action and the values of phenomenological coefficients. Using the bimetric theory we calculate the projected static structure factor up to the k6k^6 order in the momentum expansion. To provide further support for the theory, we derive the long wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. Finally, it is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism.Comment: 14 pages, v2: Acknowledgments updated, v3: A few presentation improvements, Published versio

    Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum

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    We study the spontaneous parity breaking and generating of Hall viscosity and angular momentum in holographic p+ip model, which can describe strongly-coupled chiral superfluid states in many quantum systems. The dual gravity theory, an SU(2) gauge field minimally coupled to Einstein gravity, is parity-invariant but allows a black hole solution with vector hair corresponding to a parity-broken superfluid state. We show that this state possesses a non-vanishing parity-odd transport coefficient -- Hall viscosity -- and an angular momentum density. We first develop an analytic method to solve this model near the critical regime and to take back-reactions into account. Then we solve the equation for the tensor mode fluctuations and obtain the expression for Hall viscosity via Kubo formula. We also show that a non-vanishing angular momentum density can be obtained through the vector mode fluctuations and the corresponding boundary action. We give analytic results of both Hall viscosity and angular momentum density near the critical regime in terms of physical parameters. The near-critical behavior of Hall viscosity is different from that obtained from a gravitational Chern-Simons model. We find that the magnitude of Hall viscosity to angular momentum density ratio is numerically consistent with being equal to 1/2 at large SU(2) coupling corresponding to the probe limit, in agreement with previous results obtained for various quantum fluid systems and from effective theory approaches. In addition, we find the shear viscosity to entropy density ratio remains above the universal bound.Comment: 55 pages, 1 figure. Version 2: angular momentum calculation revised; referenced adde
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