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Faugno WN, Balram AC, Barkeshli M, Jain JK. Prediction of a Non-Abelian Fractional Quantum Hall State with f-Wave Pairing of Composite Fermions in Wide Quantum Wells. PHYSICAL REVIEW LETTERS 2019; 123:016802. [PMID: 31386406 DOI: 10.1103/physrevlett.123.016802] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Indexed: 05/06/2023]
Abstract
We theoretically investigate the nature of the state at the quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian fractional quantum Hall state that is topologically equivalent to f-wave pairing of composite fermions. This state is topologically distinct from the familiar p-wave paired Pfaffian state. We compare our calculated phase diagram with experiments and make predictions for many observable quantities.
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Affiliation(s)
- W N Faugno
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Ajit C Balram
- Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Maissam Barkeshli
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20472 USA
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Balram AC, Mukherjee S, Park K, Barkeshli M, Rudner MS, Jain JK. Fractional Quantum Hall Effect at ν=2+6/13: The Parton Paradigm for the Second Landau Level. PHYSICAL REVIEW LETTERS 2018; 121:186601. [PMID: 30444400 DOI: 10.1103/physrevlett.121.186601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Indexed: 06/09/2023]
Abstract
The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν=2+6/13 [A. Kumar et al., Phys. Rev. Lett. 105, 246808 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.246808] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a "3[over ¯]2[over ¯]111" parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the 3[over ¯]2[over ¯]111 state to be a good candidate for the ν=2+6/13 FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the "n[over ¯]2[over ¯]111" family of parton states naturally describes many observed SLL FQHE plateaus.
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Affiliation(s)
- Ajit C Balram
- Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Sutirtha Mukherjee
- Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Kwon Park
- Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Maissam Barkeshli
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20472, USA
| | - Mark S Rudner
- Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - J K Jain
- Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Abstract
Abstract
In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new ‘topological’ phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase—topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems).
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Affiliation(s)
- Xiao-Gang Wen
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada
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Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons. ACTA ACUST UNITED AC 2013. [DOI: 10.1155/2013/198710] [Citation(s) in RCA: 70] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We review the progress in the last 20–30 years, during which we discovered that there are many new phases of matter that are beyond the traditional Landau symmetry breaking theory. We discuss new “topological” phenomena, such as topological degeneracy that reveals the existence of those new phases—topologically ordered phases. Just like zero viscosity defines the superfluid order, the new “topological” phenomena define the topological order at macroscopic level. More recently, we found that at the microscopical level, topological order is due to long-range quantum entanglements. Long-range quantum entanglements lead to many amazing emergent phenomena, such as fractional charges and fractional statistics. Long-range quantum entanglements can even provide a unified origin of light and electrons; light is a fluctuation of long-range entanglements, and electrons are defects in long-range entanglements.
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Qi XL, Katsura H, Ludwig AWW. General relationship between the entanglement spectrum and the edge state spectrum of topological quantum states. PHYSICAL REVIEW LETTERS 2012; 108:196402. [PMID: 23003065 DOI: 10.1103/physrevlett.108.196402] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2011] [Indexed: 05/10/2023]
Abstract
We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional conformal field theory, such as, e.g., a general quantum Hall state. We demonstrate that for such states the reduced density matrix of a finite spatial region of the gapped topological state is a thermal density matrix of the chiral edge state conformal field theory which would appear at the spatial boundary of that region. We obtain this result by applying a physical instantaneous cut to the gapped system and by viewing the cutting process as a sudden "quantum quench" into a conformal field theory, using the tools of boundary conformal field theory. We thus provide a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state.
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Affiliation(s)
- Xiao-Liang Qi
- Department of Physics, Stanford University, Stanford, California 94305, USA
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Wen XG. Continuous topological phase transitions between clean quantum hall states. PHYSICAL REVIEW LETTERS 2000; 84:3950-3953. [PMID: 11019247 DOI: 10.1103/physrevlett.84.3950] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/1999] [Indexed: 05/23/2023]
Abstract
Continuous transitions between states and the same symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral nonbosonic quasiparticles are shown to have such transitions under the right conditions. For clean bilayer (mmn) states, a continuous transition to other QH states (including non-Abelian states) can be driven by increasing interlayer repulsion/tunneling. The effective theories describing the critical points at some transitions are obtained.
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Affiliation(s)
- XG Wen
- Department of Physics and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Nagaosa N, Kohmoto M. Edge and Bulk of the Fractional Quantum Hall Liquids. PHYSICAL REVIEW LETTERS 1995; 75:4294-4297. [PMID: 10059868 DOI: 10.1103/physrevlett.75.4294] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Wen XG. Impurity effects on chiral one-dimensional electron systems. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:5420-5428. [PMID: 9976884 DOI: 10.1103/physrevb.50.5420] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Lee DH, Wen XG. Orbital spins of the collective excitations in Hall liquids. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:11066-11070. [PMID: 10009953 DOI: 10.1103/physrevb.49.11066] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Pokrovsky VL, Pryadko LP. Quasi Fermi distribution and resonant tunneling of quasiparticles with fractional charges. PHYSICAL REVIEW LETTERS 1994; 72:124-127. [PMID: 10055582 DOI: 10.1103/physrevlett.72.124] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Kol A, Read N. Fractional quantum Hall effect in a periodic potential. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:8890-8898. [PMID: 10007108 DOI: 10.1103/physrevb.48.8890] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Zang J, Birman JL. Farey series, hierarchy structure, and scaling theory of the fractional quantum Hall effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:16305-16310. [PMID: 10006056 DOI: 10.1103/physrevb.47.16305] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Li D. Hierarchical wave function, Fock cyclic condition, and spin-statistics relation in the spin-singlet fractional quantum Hall effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:13370-13379. [PMID: 10005645 DOI: 10.1103/physrevb.47.13370] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wen XG. Resonant tunneling in the fractional quantum Hall regime. PHYSICAL REVIEW LETTERS 1993; 70:2605-2608. [PMID: 10053605 DOI: 10.1103/physrevlett.70.2605] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Wen XG. Topological order and edge structure of nu =1/2 quantum Hall state. PHYSICAL REVIEW LETTERS 1993; 70:355-358. [PMID: 10054091 DOI: 10.1103/physrevlett.70.355] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Chen W, Semenoff GW, Wu YS. Two-loop analysis of non-Abelian Chern-Simons theory. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1992; 46:5521-5539. [PMID: 10014944 DOI: 10.1103/physrevd.46.5521] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wen XG. Edge transport properties of the fractional quantum Hall states and weak-impurity scattering of a one-dimensional charge-density wave. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:5708-5719. [PMID: 9998414 DOI: 10.1103/physrevb.44.5708] [Citation(s) in RCA: 129] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wen XG, Zee A. Topological structures, universality classes, and statistics screening in the anyon superfluid. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:274-284. [PMID: 9998244 DOI: 10.1103/physrevb.44.274] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wen XG. Gapless boundary excitations in the quantum Hall states and in the chiral spin states. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:11025-11036. [PMID: 9996836 DOI: 10.1103/physrevb.43.11025] [Citation(s) in RCA: 168] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Blok B, Wen XG. Structure of the microscopic theory of the hierarchical fractional quantum Hall effect. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 43:8337-8349. [PMID: 9996464 DOI: 10.1103/physrevb.43.8337] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wen XG. Non-Abelian statistics in the fractional quantum Hall states. PHYSICAL REVIEW LETTERS 1991; 66:802-805. [PMID: 10043904 DOI: 10.1103/physrevlett.66.802] [Citation(s) in RCA: 57] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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