Composite-fermion Hall conductance at ν=

Kivelson, Steven; Lee, D.-H.; Krotov, Yu. A.; Gan, Junwu

doi:10.1103/physrevb.55.15552

Cited by 65 publications

(86 citation statements)

References 25 publications

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“…With a two-body interaction (e.g., Coulomb) the resulting Hamiltonian has a "particle-hole" symmetry at ν = 1 2 . This symmetry is not manifest in the HLR description of the composite fermi liquid, and is possibly even violated by it [17,18]. A lowest Landau level description is often routinely used in theoretical discussions and numerical calculations of quantum hall states, including at ν = thus important to understand how the particle-hole symmetry should be incorporated into the theory of the composite Fermi liquid.…”

Section: A the Half-filled Landau Levelmentioning

confidence: 99%

“…It has been appreciated for some time [17,18] that the effective field theory proposed by HLR for the half-filled Landau level is not manifestly particle-hole symmetric, and is perhaps even inconsistent with it. On the other hand, numerical calculations performed in the lowest Landau level show that with the projected two-body Coulomb interaction the Fermi-liquid-like state at half-filling preserves particlehole symmetry (see, for instance, Ref.…”

Section: Particle-hole Symmetry and The Composite Fermi Liquidmentioning

confidence: 99%

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Half-filled Landau level, topological insulator surfaces, and three-dimensional quantum spin liquids

Wang¹,

Senthil²

2016

Phys. Rev. B

104

173

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We synthesize and partly review recent developments relating the physics of the half-filled Landau level in two dimensions to correlated surface states of topological insulators in three dimensions. The latter are in turn related to the physics of certain three-dimensional quantum spin liquid states. The resulting insights provide an interesting answer to the old question of how particle-hole symmetry is realized in composite fermion liquids. Specifically the metallic state at filling ν = 1 2 -described originally in pioneering work by Halperin, Lee, and Read as a liquid of composite fermions-was proposed recently by Son to be described by a particle-hole symmetric effective field theory distinct from that in the prior literature. We show how the relation to topological insulator surface states leads to a physical understanding of the correctness of this proposal. We develop a simple picture of the particle-hole symmetric composite fermion through a modification of older pictures as electrically neutral "dipolar" particles. We revisit the phenomenology of composite fermi liquids (with or without particle-hole symmetry), and show that their heat/electrical transport dramatically violates the conventional Wiedemann-Franz law but satisfies a modified one. We also discuss the implications of these insights for finding physical realizations of correlated topological insulator surfaces.

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Section: A the Half-filled Landau Levelmentioning

confidence: 99%

Section: Particle-hole Symmetry and The Composite Fermi Liquidmentioning

confidence: 99%

Half-filled Landau level, topological insulator surfaces, and three-dimensional quantum spin liquids

Wang¹,

Senthil²

2016

Phys. Rev. B

104

173

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“…(11). In terms of the structure of the eigen wave functions, the orthogonality, completeness, and closeness are obvious.…”

Section: Cmentioning

confidence: 99%

“…While Majonara fermion is a fully relativistic object 7 , Moore-Read Pfaffian is the variational ground state wave function of a two-dimensional nonrelativistic electron gas in a strong external magnetic field 8 . The seminal Halperin-Lee-Read (HLR) composite Fermi liquid (CFL) theory 1 furnished a good venue to study this p-wave pairing state 10 but the non-relativistic nature of HLR theory and the breakdown of the particlehole symmetry (PHS) 11,12 block to clarify this ambiguity. Therefore, a relativistic CFL theory is eagerly called together with the following facts: The PHS of Jain's sequences of FQHE 13 ; the PHS wave function for ν = state shown by numerical calculations 14 ; as well as the requirement of the universal origin for 1 2 anomalous Hall conductivity in ν = 1 2 CFL 11,12 .…”

Section: Introductionmentioning

confidence: 99%

“…The seminal Halperin-Lee-Read (HLR) composite Fermi liquid (CFL) theory 1 furnished a good venue to study this p-wave pairing state 10 but the non-relativistic nature of HLR theory and the breakdown of the particlehole symmetry (PHS) 11,12 block to clarify this ambiguity. Therefore, a relativistic CFL theory is eagerly called together with the following facts: The PHS of Jain's sequences of FQHE 13 ; the PHS wave function for ν = state shown by numerical calculations 14 ; as well as the requirement of the universal origin for 1 2 anomalous Hall conductivity in ν = 1 2 CFL 11,12 . Recently, the enthusiasm of research for reexamining the CFL theory is aroused by experiments [15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

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Nonperturbative emergence of the Dirac fermion in a strongly correlated composite Fermi liquid

Yang¹,

Luo²,

Yu³

2017

Phys. Rev. B

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The classic composite fermion field theory 1 builds up an excellent framework to uniformly study important physical objects and globally explain anomalous experimental phenomena in fractional quantum Hall physics while there are also inherent weaknesses. We present a nonperturbative emergent Dirac fermion theory from this strongly correlated composite fermion field theory, which overcomes these serious long-standing shortcomings. The particle-hole symmetry of Dirac equation resolves this particle-hole symmetry enigma in the composite fermion field theory. With the help of presented numerical data, we show that for main Jain's sequences of fractional quantum Hall effects, this emergent Dirac fermion theory in mean field approximation is most likely stable.

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Duality between (2+1)d quantum critical points

et al. 2019

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Duality refers to two equivalent descriptions of the same theory from different points of view. Recently there has been tremendous progress in formulating and understanding possible dualities of quantum many body theories in 2 + 1-spacetime dimensions. Of particular interest are dualities that describe conformally invariant quantum field theories in (2 + 1)d. These arise as descriptions of quantum critical points in condensed matter physics. The appreciation of the possible dual descriptions of such theories has greatly enhanced our understanding of some challenging questions about such quantum critical points. Perhaps surprisingly the same dualities also underlie recent progress in our understanding of other problems such as the half-filled Landau level and correlated surface states of topological insulators. Here we provide a pedagogical review of these recent developments from a point of view geared toward condensed matter physics.

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Composite-fermion Hall conductance at ν=

Cited by 65 publications

References 25 publications

Half-filled Landau level, topological insulator surfaces, and three-dimensional quantum spin liquids

Half-filled Landau level, topological insulator surfaces, and three-dimensional quantum spin liquids

Nonperturbative emergence of the Dirac fermion in a strongly correlated composite Fermi liquid

Duality between (2+1)d quantum critical points

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