This article was accepted into the corpus but its outbound wikilinks were never NER-processed — typical at the deepest BFS hop or when the run's entity cap was reached. No expansion funnel to show.
| Moore–Read Pfaffian state | |
|---|---|
| Name | Moore–Read Pfaffian state |
| Other names | Pfaffian state, Moore–Read state |
| Field | Condensed matter physics |
| Discovered | 1991 |
| Discoverers | Gregory Moore; Nicholas Read |
| Related | Fractional quantum Hall effect; Non-Abelian anyons; Topological order |
Moore–Read Pfaffian state. The Moore–Read Pfaffian state is a proposed topologically ordered quantum state proposed for two-dimensional electron systems under strong magnetic fields, introduced by Gregory Moore and Nicholas Read as a candidate for the fractional quantum Hall effect at filling factor 5/2; it connects ideas from Conformal field theory, Read–Rezayi states, Pfaffian (matrix) structures, and non-Abelian statistics in a framework influential across condensed matter physics, quantum computation, and mathematical physics.
The Moore–Read Pfaffian state was introduced in 1991 by Gregory Moore and Nicholas Read as a trial wavefunction for the fractional quantum Hall effect at even-denominator filling, motivated by connections to Ising model (statistical mechanics), conformal blocks, and the Virasoro algebra; it proposed that the observed 5/2 plateau in the Quantum Hall effect could host quasiparticles obeying non-Abelian anyons statistics. The proposal immediately linked to developments by Robert Laughlin on correlated states, to numerical studies by F. D. M. Haldane and E. H. Rezayi, and to theoretical constructions related to topological quantum field theory, Chern–Simons theory, and the pursuit of fault-tolerant quantum computation using anyons.
The Moore–Read Pfaffian wavefunction is built from a Pfaffian factor multiplying a Laughlin wavefunction-like Jastrow factor, with the Pfaffian encoding pairing similar to BCS pairing in superconductivity and the Jastrow factor enforcing correlations familiar from work by Robert Laughlin and David J. Thouless; the original construction drew on conformal field theory methods developed by Alexander Zamolodchikov and others to express wavefunctions as correlators of primary fields in the Ising conformal field theory. Mathematically the Pfaffian is the square root of a determinant (linear algebra), and in the Moore–Read context it implements a paired composite-fermion picture related to the composite-fermion theory of Jainendra K. Jain and numerical exact diagonalization studies by N. Read and E. H. Rezayi. The state can be generalized to spinful, multilayer, and higher Landau level constructions, building on formalism from Halperin (state), Read–Rezayi states, and algebraic structures linked to parafermions and the Wess–Zumino–Witten model.
Quasiparticle excitations of the Moore–Read Pfaffian state carry fractional charge and exhibit non-Abelian braiding, predicted to implement Ising-type fusion rules related to Majorana fermions and the zero modes studied in contexts like Kitaev chain and proposals by Alexei Kitaev for topological quantum computation; the non-Abelian statistics were analyzed using techniques from Chern–Simons theory by Edward Witten and by mapping to conformal-block monodromies from Moore and Read. The state supports edge modes described by a chiral boson plus an Ising conformal field theory sector, connecting to edge theories developed by Xiao-Gang Wen and tunneling phenomenology measured in experiments guided by work from Robert Willett and C. L. Kane. Thermal Hall conductance, ground-state degeneracy on higher-genus surfaces, and fusion-channel-dependent interferometry outcomes are key signatures tied to the mathematical classification of topological orders by Kitaev (2006), Wen (1990s), and subsequent categorizations using modular tensor categories.
The Moore–Read Pfaffian state is most closely associated with the experimentally observed 5/2 fractional quantum Hall plateau first reported by R. R. Willett and collaborators, and has motivated shot-noise, tunneling, and interferometry experiments by groups led by Chetan Nayak, Michael Heiblum, and Laurens Molenkamp seeking fractional charge and non-Abelian braiding signatures; experiments measuring quasiparticle charge, upstream neutral modes, and thermal conductance have been interpreted in light of competing proposals by N. Read and E. Rezayi as either supporting the Pfaffian, its particle-hole conjugate (the anti-Pfaffian), or other Abelian and non-Abelian states. High-mobility two-dimensional electron gas systems in GaAs/AlGaAs heterostructures and proposals for platforms in graphene, ZnO heterostructures, and topological insulator interfaces have been explored, informed by sample fabrication advances at institutions like Bell Labs and research by groups at Princeton University and Caltech.
The Moore–Read Pfaffian state spawned a family of theoretical extensions including the Read–Rezayi sequence, parafermionic states, and paired composite-fermion constructions developed by N. Read, E. H. Rezayi, and B. A. Bernevig; competing proposals for the 5/2 plateau include the anti-Pfaffian, proposed by Levin, Halperin, and Rosenow-style analyses, Abelian hierarchical states influenced by Haldane (1983) ideas, and composite-fermion paired states tied to work by Jain. Field-theoretic descriptions link the Pfaffian to SU(2)_2 Chern–Simons theory, to Ising modular tensor categories studied by Moore and Seiberg, and to lattice realizations considered in the context of Kitaev honeycomb model research. Ongoing theoretical work explores disorder effects analyzed by Simon (2007) and Feldman, entanglement spectra techniques pioneered by Haldane and Li & Haldane, and applications to fault-tolerant topological quantum computation pursued by Nayak and collaborators.
Category:Fractional quantum Hall states