New Class of Non-Abelian Spin-Singlet Quantum Hall States

Ardonne, Eddy; Schoutens, Kareljan

doi:10.1103/physrevlett.82.5096

Cited by 148 publications

(274 citation statements)

References 26 publications

(40 reference statements)

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“…We applied this procedure to the non-abelian spin singlet states of [10] (the explicit form of the wave functions will be given elsewhere [25]), and indeed found the same results for the electron and spin filling factor as obtained from the K-matrix formalism, Eq. (7.1).…”

Section: 1mentioning

confidence: 59%

“…Our analysis here builds on earlier results published in [9,10,11,12,13]. In [14] we presented our present results in brief form, and elaborated on the physical meaning of the newly obtained K-matrices.…”

Section: Introductionmentioning

confidence: 57%

“…The matrix K e , related to K φ by the duality K e = K −1 φ , refers to particles which are identified as composites of the fundamental electron-like excitation. From the point of view of the wave functions for the nonabelian quantum Hall states [2,23,10], the presence of composite excitations is very natural. This is because the non-abelian states show a behaviour which is called clustering (of order k, where k is a label of the states [23,10]).…”

Section: 1mentioning

confidence: 99%

“…From the point of view of the wave functions for the nonabelian quantum Hall states [2,23,10], the presence of composite excitations is very natural. This is because the non-abelian states show a behaviour which is called clustering (of order k, where k is a label of the states [23,10]). This order-k clustering means that up to k particles can come to the same position, without making the wave function zero, whereas, as soon as k + 1 particles are located at the same positions, the wave function becomes identically zero.…”

Section: 1mentioning

confidence: 99%

“…The IOW-equation for µ tot = µ ↑ µ ↓ , resulting from (7.9), is given by 10) and is dual to (7.5) in the sense of (4.3). Explicitly,…”

Section: ( Slmentioning

confidence: 99%

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Ardonne

Bouwknegt

Schoutens

2001

Journal of Statistical Physics

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Abstract. We study excitations in edge theories for non-abelian 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 edge-electrons and edge-quasiholes, we arrive at a novel K-matrix structure. Interestingly, the duality between the electron and quasihole sectors links the pseudoparticles that are characteristic for non-abelian statistics with composite particles that are associated to the 'pairing physics' of the nonabelian quantum Hall states.

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Section: 1mentioning

confidence: 59%

Section: Introductionmentioning

confidence: 57%

Section: 1mentioning

confidence: 99%

Section: 1mentioning

confidence: 99%

“…The IOW-equation for µ tot = µ ↑ µ ↓ , resulting from (7.9), is given by 10) and is dual to (7.5) in the sense of (4.3). Explicitly,…”

Section: ( Slmentioning

confidence: 99%

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Ardonne

Bouwknegt

Schoutens

2001

Journal of Statistical Physics

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Paired and Clustered Quantum Hall States

Schoutens

Ardonne

Lankvelt

2002

Statistical Field Theories

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Infinite Dimensional Matrix Product States for Long-Range Quantum Spin Models

Bondesan

Quella

2016

Springer Proceedings in Mathematics &Amp; Statistics

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We construct 1D and 2D long-range SU(N ) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N ) 1 WZW model. Since the resulting groundstates are of Gutzwiller-Jastrow type, our models can be regarded as lattice discretizations of fractional quantum Hall systems. We then focus on two specific types of 1D spin chains with spins located on the unit circle, a uniform and an alternating arrangement. For an equidistant distribution of identical spins we establish an explicit connection to the SU(N ) Haldane-Shastry model, thereby proving that the model is critical and described by a SU(N ) 1 WZW model. In contrast, while turning out to be critical as well, the alternating model can only be treated numerically. Our numerical results rely on a reformulation of the original problem in terms of loop models. IntroductionLong-range spin models such as the Gaudin model [1] or the Haldane-Shastry model [2,3] have attracted the attention of physicists and mathematicians for a long period of time. In its original formulation, the Haldane-Shastry model describes the dynamics of SU(2) spins on a circle with inverse distance square interactions. It received a lot of attention due to its exact solvability and due to the form of its groundstate which is closely related to a bosonic Laughlin wavefunction at filling fraction ν = 1/2. The Haldane-Shastry model can be viewed as realizing a 1D analogue of a chiral spin liquid, with spinon excitations satisfying a generalized Pauli exclusion principle and obeying fractional statistics [4]. Many of the remarkable properties of the Haldane-Shastry model have their origin in the existence of an infinite-dimensional Yangian symmetry [5]. The latter also allowed to identify its thermodynamic limit as the SU(2) WZW conformal field theory at level k = 1 [6] (see also [7]). The Haldane-Shastry model admits obvious generalizations to symmetry groups such as the unitary series SU(N ) [5] or its supersymmetric analog SU(M |N ) [8,9].For our current work, there are two aspects of the SU(N ) Haldane-Shastry model that will be particularly important. First of all, it provides an efficient discretization of the SU(N ) WZW conformal field theory at level k = 1, where the scaling laws are not affected by logarithmic corrections. Secondly, wavefunctions of the groundstate as well as the excited states exhibit an intimate relation to the physics of fractional quantum Hall (FQH) systems, also for general values of N [10]. There are of course also differences: While the constituents of FQH systems are particles which are moving on a 2D surface, the degrees of freedom in the spin model are pinned to fixed discrete locations on a circle.The study of fractional quantum Hall systems is frequently based on the following intriguing dichotomy: One single chiral 2D conformal field theory (CFT) describes the two complementary aspects of the physical sample -its bulk and its boundary. It is known since the work of Mo...

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New Class of Non-Abelian Spin-Singlet Quantum Hall States

Cited by 148 publications

References 26 publications

Untitled

Untitled

Paired and Clustered Quantum Hall States

Infinite Dimensional Matrix Product States for Long-Range Quantum Spin Models

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