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

Gočanin, Dragoljub; Predin, Sonja; Ćirić, Marija Dimitrijević; Radovanović, Voja; Milovanović, Milica

doi:10.48550/arxiv.2102.11313

Cited by 3 publications

(4 citation statements)

References 15 publications

(28 reference statements)

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“…Our conclusions overlap in the way that PH Pfaffian correlations can be viewed as a s − wave pairing of composite fermion and composite hole -the concept that was introduced in Ref. [15] which gives a microscopic derivation of the Dirac composite fermion theory. The geometry of the numerical work in [33] is the geometry of sphere, which may be biased towards particular insta-bilities, while the geometry of the numerical experiment in [19] is the torus geometry (which does not have that bias but may be disadvantageous in other ways).…”

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confidence: 66%

“…i.e. sources are what we may call composite fermion (CF) -composite of electron and correlation hole, represented by field c (a component of the Dirac spinor) and composite hole -a composite of hole and its "correlation particle", represented by a field d (another component of the Dirac spinor) [15]. It is interesting to note that with the two degrees of freedom we have possibility for "intra" pairing (Pfaffian and anti-Pfaffian) and "inter" pairing (PH Pfaffian).…”

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confidence: 99%

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PH Pfaffian intra and inter correlations in the quantum Hall bilayer

Milovanovic,

Djurdjevic

2021

Preprint

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PH Pfaffian topological phase may exist in a uniform system due to strong Landau level (LL) mixing according to theoretical predictions based on the Son -Dirac composite fermion theory. Numerical investigations in the presence of large LL mixing are limited due to numerical complexities, when taking into account at least one more LL. Because of this, we apply the same field theoretical approach to the quantum Hall bilayer at total filling factor equal to one, for which many numerical studies exist. The most advanced in [19] predicts an intermediate phase (for intermediate distances between layers) with an even-odd effect. According to our approach, the intermediate phase represents a mixed negative-flux p-wave pairing i.e. coexisting intra (PH Pfaffian in each layer) and inter (a la PH Pfaffian) pairing correlations. This again underlines a necessity for strong entanglement with additional degrees of freedom, i.e. at least one more (additional) LL in the search for a stable PH Pfaffian phase in a single layer. Based on the analogy with the bilayer physics we propose a PH Pfaffian wave function that resides in two LLs.

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confidence: 66%

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confidence: 99%

PH Pfaffian intra and inter correlations in the quantum Hall bilayer

Milovanovic,

Djurdjevic

2021

Preprint

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“…Microscopic wave functions prescribed by the theory of CFs are well tested and widely accepted as precise descriptions of many-body states of fractionally filled LLs [23]. The fact that the dipole picture is directly inferred from a microscopic wave function distinguishes it from the HLR theory and the Dirac CF theory, both of which are based on conjectured effective field theories and cannot be directly associated with actual microscopic wave functions except for a few special cases [24][25][26][27].…”

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confidence: 99%

Emergence of Dirac composite fermions: Dipole picture

Shi

2021

Phys. Rev. Research

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Composite fermions (CFs) are the particles underlying the novel phenomena observed in partially filled Landau levels. Both microscopic wave functions and semi-classical dynamics suggest that a CF is a dipole consisting of an electron and a double 2h/e quantum vortex, and its motion is subject to a Berry curvature that is uniformly distributed in the momentum space. Based on the picture, we study the electromagnetic response of composite fermions. We find that the response in the long-wavelength limit has a form identical to that of the Dirac CF theory. To obtain the result, we show that the Berry curvature contributes a half-quantized Hall conductance which, notably, is independent of the filling factor of a Landau level and not altered by the presence of impurities. The latter is because CFs undergo no side-jumps when scattered by quenched impurities in a Landaulevel with the particle-hole symmetry. The remainder of the response is from an effective system that has the same Fermi wavevector, effective density, Berry phase, and therefore long-wavelength response to electromagnetic fields as a Dirac CF system. By interpreting the half-quantized Hall conductance as a contribution from a redefined vacuum, we can explicitly show the emergence of a Dirac CF effective description from the dipole picture. We further determine corrections due to electric quadrupoles and magnetic moments of CFs and show deviations from the Dirac CF theory when moving away from the long wavelength limit.

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“…In the rest of this paper we will build on these results and describe the physics of the model 1 A proposal for a non-commutative field theory for fermions at ν = 1/2 has recently appeared [26]. in Eqn.…”

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confidence: 99%

Evolution between quantum Hall and conducting phases: simple models and some results

Dong,

Senthil

2021

Preprint

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Quantum many particle systems in which the kinetic energy, strong correlations, and band topology are all important pose an interesting and topical challenge. Here we introduce and study particularly simple models where all of these elements are present. We consider interacting quantum particles in two dimensions in a strong magnetic field such that the Hilbert space is restricted to the Lowest Landau Level (LLL) . This is the familiar quantum Hall regime with rich physics determined by the particle filling and statistics. A periodic potential with a unit cell enclosing one flux quantum broadens the LLL into a Chern band with a finite bandwidth. The states obtained in the quantum Hall regime evolve into conducting states in the limit of large bandwidth. We study this evolution in detail for the specific case of bosons at filling factor ν = 1. In the quantum Hall regime the ground state at this filling is a gapped quantum hall state (the "bosonic Pfaffian") which may be viewed as descending from a (bosonic) composite fermi liquid. At large bandwidth the ground state is a bosonic superfluid. We show how both phases and their evolution can be described within a single theoretical framework based on a LLL composite fermion construction. Building on our previous work on the bosonic composite fermi liquid, we show that the evolution into the superfluid can be usefully described by a noncommutative quantum field theory in a periodic potential. Contents I. Introduction 2II. Review of non-commutative theory for composite fermi liquids 8

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

Cited by 3 publications

References 15 publications

PH Pfaffian intra and inter correlations in the quantum Hall bilayer

PH Pfaffian intra and inter correlations in the quantum Hall bilayer

Emergence of Dirac composite fermions: Dipole picture

Evolution between quantum Hall and conducting phases: simple models and some results

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