Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities

Gočanin, Dragoljub; Predin, Sonja; Ćirić, Marija Dimitrijević; Radovanovic, Voja; Milovanović, M. V.

doi:10.1103/physrevb.104.115150

Cited by 13 publications

(4 citation statements)

References 23 publications

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“…[73]). A non-commutative, LLL field theory of the ν = 1/2 state was proposed recently [74], but further work is needed in this direction.…”

Section: Discussionmentioning

confidence: 99%

Lowest Landau level theory of the bosonic Jain states

Goldman,

Senthil

2021

Preprint

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Quantum Hall systems offer the most familiar setting where strong inter-particle interactions combine with the topology of single particle states to yield novel phenomena. Despite our mature understanding of these systems, an open challenge has been to to develop a microscopic theory capturing both their universal and non-universal properties, when the Hamiltonian is restricted to the non-commutative space of the lowest Landau level. Here we develop such a theory for the Jain sequence of bosonic fractional quantum Hall states at fillings ν = p p+1 . Building on a lowest Landau level description of a parent composite fermi liquid at ν = 1, we describe how to dope the system to reach the Jain states. Upon doping, the composite fermions fill non-commutative generalizations of Landau levels, and the Jain states correspond to integer composite fermion filling. Using this approach, we obtain an approximate expression for the bosonic Jain sequence gaps with no reference to any long-wavelength approximation. Furthermore, we show that the universal properties, such as Hall conductivity, are encoded in an effective non-commutative Chern-Simons theory, which is obtained on integrating out the composite fermions. This theory has the same topological content as the familiar Abelian Chern-Simons theory on commutative space.

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“…[73]). A non-commutative, LLL field theory of the ν = 1/2 state was proposed recently [74], but further work is needed in this direction.…”

Section: Discussionmentioning

confidence: 99%

Lowest Landau level theory of the bosonic Jain states

Goldman,

Senthil

2021

Preprint

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“…This is captured by replacing the multiplication between ordinary fields with the Moyal-Weyl star product ⋆ [16,17]. In the present case, we have [19] c(x) ⋆ c(y…”

Section: Non-commutative Field Theory and Gauge Fluctuationsmentioning

confidence: 96%

“…Hence, the approximation by the HLR theory is justified in the long-wavelength regime and the fluctuation in gauge field has a small amplitude. The above approach has been applied in a series of recent work in studying quantum Hall physics and related topics [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Quantitative theory of composite fermions in Bose-Fermi mixtures at $ν=1$

Ma,

Yang

2021

Preprint

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“…Such noncommutative field theory of the half-filled Landau level can be constructed (see, e.g., Ref. [16]) but one sees an immediate problem. Namely, the NC U (1) a gauge symmetry is in conflict with the particle-hole (PH) symmetry (or CT symmetry) of the physics on a single Landau level.…”

Section: Noncommutative Symmetry In Effective Field Theorymentioning

confidence: 99%

Noncommutative gauge symmetry in the fractional quantum Hall effect

Du¹,

Mehta²,

Son³

2021

Preprint

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We show that a system of particles on the lowest Landau level can be coupled to a probe U(1) gauge field A µ in such a way that the theory is invariant under a noncommutative U(1) gauge symmetry. While the temporal component A 0 of the probe field is coupled to the projected density operator, the spatial components A i are best interpreted as quantum displacements, which distort the interaction potential between the particles. We develop a Seiberg-Witten-type map from the noncommutative U(1) gauge symmetry to a simpler version, which we call "baby noncommutative" gauge symmetry, where the Moyal brackets are replaced by the Poisson brackets. The latter symmetry group is isomorphic to the group of volume preserving diffeomorphisms.By using this map, we resolve the apparent contradiction between the noncommutative gauge symmetry, on the one hand, and the particle-hole symmetry of the half-filled Landau level and the presence of the mixed Chern-Simons terms in the effective Lagrangian of the fractional quantum Hall states, on the other hand. We outline the general procedure which can be used to write down effective field theories which respect the noncommutative U(1) symmetry.

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Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities

Cited by 13 publications

References 23 publications

Lowest Landau level theory of the bosonic Jain states

Lowest Landau level theory of the bosonic Jain states

Quantitative theory of composite fermions in Bose-Fermi mixtures at $ν=1$

Noncommutative gauge symmetry in the fractional quantum Hall effect

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