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29
Anyons in an exactly solved model and beyond
, 2005
"... A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge f ..."
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Cited by 27 (2 self)
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A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are nonAbelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number ν. The Abelian and nonAbelian phases of the original model correspond to ν = 0 and ν = ±1, respectively. The anyonic properties of excitation depend on ν mod 16, whereas ν itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
Nonabelian anyons and topological quantum computation
 Reviews of Modern Physics
"... Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are partic ..."
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Cited by 10 (0 self)
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Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles,
Unpaired majorana fermions in quantum wires
, 2000
"... Certain onedimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possesses two ground states with an energy difference proportional to exp(−L/l0) and different fermionic parities ..."
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Cited by 7 (3 self)
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Certain onedimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possesses two ground states with an energy difference proportional to exp(−L/l0) and different fermionic parities. Such systems can be used as qubits since they are intrinsically immune to decoherence. The property of a system to have boundary Majorana fermions is expressed as a condition on the bulk electron spectrum. The condition is satisfied in the presence of an arbitrary small energy gap induced by proximity of a 3dimensional pwave superconductor, provided that the normal spectrum has an odd number of Fermi points in each half of the Brillouin zone (each spin component counts separately).
NonAbelian Anyons and Topological Quantum Computation. arxiv: condmat.strel/0707.1889
"... Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are partic ..."
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Cited by 7 (1 self)
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Contents Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a faulttolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as NonAbelian anyons, meaning that they obey nonAbelian braiding statistics. Quantum information is stored in states with multiple quasiparticles,
NonAbelian quantum Hall states – exclusion statistics, Kmatrices and duality
, 2000
"... We study excitations in edge theories for nonabelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edgeelectrons and edgequasiholes, we arr ..."
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Cited by 6 (3 self)
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We study excitations in edge theories for nonabelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edgeelectrons and edgequasiholes, we arrive at a novel Kmatrix structure. Interestingly, the duality between the electron and quasihole sectors links the pseudoparticles that are characteristic for nonabelian statistics with composite particles that are associated to the ‘pairing physics’ of the nonabelian quantum Hall states.
Disordered 2d quasiparticles in class d: Dirac fermions with random mass, and dirty superconductors
 Nuclear Physics B
"... fermions with random mass, and dirty superconductors ..."
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Cited by 5 (0 self)
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fermions with random mass, and dirty superconductors
ARTICLES Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2
, 2007
"... Recent theories suggest that the quasiparticles that populate certain quantum Hall states should exhibit exotic braiding statistics that could be used to build topological quantum gates. Confined systems that support such states at a filling fraction ν = 5/2 are of particular interest for testing th ..."
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Cited by 5 (0 self)
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Recent theories suggest that the quasiparticles that populate certain quantum Hall states should exhibit exotic braiding statistics that could be used to build topological quantum gates. Confined systems that support such states at a filling fraction ν = 5/2 are of particular interest for testing these predictions. Here, we report transport measurements of just such a system, which consists of a quantum point contact (QPC) in a twodimensional GaAs/AlGaAs electron gas that itself exhibits a welldeveloped fractional quantum Hall effect at a bulk filling fraction ν bulk = 5/2. We observe plateaulike features at an effective filling fraction of ν QPC = 5/2 for lithographic contact widths of 1.2 µm and 0.8 µm, but not 0.5 µm. Transport near ν QPC = 5/2 in the QPCs is consistent with a picture of chiral Luttingerliquid edge states with interedge tunnelling, suggesting that an incompressible state at ν QPC = 5/2 forms in this confined geometry. The discovery 1 of a fractional quantum Hall effect (FQHE) at the evendenominator filling fraction ν = 5/2 has sparked a series of experimental 2–6 and theoretical 7–9 studies, leading to a prevailing interpretation of the 5/2 state as comprising paired fermions condensed into a Bardeen–Cooper–Schriefferlike state 10–13. Within this picture, excitations of the 5/2 ground state possess nonabelian statistics 14–16 and associated topological properties. The possibility
Kmatrices for nonAbelian quantum Hall states, Phys
 Rev. B
"... Two fundamental aspects of socalled nonabelian quantum Hall states (the qpfaffian states and more general) are a (generalized) pairing of the participating electrons and the nonabelian statistics of the quasihole excitations. In this paper, we show that these two aspects are linked by a duality ..."
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Cited by 4 (4 self)
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Two fundamental aspects of socalled nonabelian quantum Hall states (the qpfaffian states and more general) are a (generalized) pairing of the participating electrons and the nonabelian statistics of the quasihole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the Kmatrices that describe the exclusion statistics of the fundamental excitations in these systems.
Periodic table for topological insulators and superconductors
, 901
"... Abstract. Gapped phases of noninteracting fermions, with and without charge conservation and timereversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of re ..."
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Cited by 4 (0 self)
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Abstract. Gapped phases of noninteracting fermions, with and without charge conservation and timereversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z2. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of Khomology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the Ktheoretic classification is stable to interactions, but a counterexample is also given. Keywords: Topological phase, Ktheory, Khomology, Clifford algebra, Bott periodicity