Abstract We study explicit model wave functions describing the fundamental quasiholes in a class of non-Abelian fractional quantum Hall states. This class is a family of paired spin-singlet states with internal degrees of freedom. We determine the braid statistics of the quasiholes by determining the monodromy of the explicit quasihole wave functions, that is how they transform under exchanges of quasihole coordinates. The statistics is shown to be the same as that of the quasiholes in the Read–Rezayi states, up to a phase. We also discuss the application of this result to a class of non-Abelian hierarchy wave functions.Abstract We study explicit model wave functions describing the fundamental quasiholes in a class of non-Abelian fractional quantum Hall states. This class is a family of paired spin-singlet states with internal degrees of freedom. We determine the braid statistics of the quasiholes by determining the monodromy of the explicit quasihole wave functions, that is how they transform under exchanges of quasihole coordinates. The statistics is shown to be the same as that of the quasiholes in the Read–Rezayi states, up to a phase. We also discuss the application of this result to a class of non-Abelian hierarchy wave functions.

arXiv:1906.01919Journal of Physics A Mathematical and TheoreticalDec 9, 20192 citations

Non-Abelian quantum Hall states of fermions and bosons

N. Read

Bulletin of the American Physical SocietyMar 5, 20070 citations

Structure of spinful quantum Hall states: A squeezing perspective

Eddy Ardonne, Nicolas Regnault

We provide a set of rules to define several spinful quantum Hall model states. The method extends the one that is known for spin-polarized states. It is achieved by specifying an undressed root partition, a squeezing procedure, and rules to dress the configurations with spin. It applies to both the excitationless and the quasihole states. In particular, we show that the naive generalization where one preserves the spin information during the squeezing sequence may fail. We give numerous examples such as the Halperin states, the non-Abelian spin-singlet states, or the spin-charge separated states. The squeezing procedure for the series $(k=2,r)$ of spinless quantum Hall states, which vanish as $r$ powers when $k+1$ particles coincide, is generalized to the spinful case. As an application of our method, we show that the counting observed in the particle entanglement spectrum of several spinful states matches the one obtained through the root partitions and our rules. This counting also matches the counting of quasihole states of the corresponding model Hamiltonians, when the latter are available.We provide a set of rules to define several spinful quantum Hall model states. The method extends the one that is known for spin-polarized states. It is achieved by specifying an undressed root partition, a squeezing procedure, and rules to dress the configurations with spin. It applies to both the excitationless and the quasihole states. In particular, we show that the naive generalization where one preserves the spin information during the squeezing sequence may fail. We give numerous examples such as the Halperin states, the non-Abelian spin-singlet states, or the spin-charge separated states. The squeezing procedure for the series $(k=2,r)$ of spinless quantum Hall states, which vanish as $r$ powers when $k+1$ particles coincide, is generalized to the spinful case. As an application of our method, we show that the counting observed in the particle entanglement spectrum of several spinful states matches the one obtained through the root partitions and our rules. This counting also matches the counting of quasihole states of the corresponding model Hamiltonians, when the latter are available.

arXiv:1107.2232Physical Review BNov 21, 201132 citations

Topological Entanglement in Abelian and Non-Abelian Excitation Eigenstates

Zlatko Papić, Bogdan Andrei Bernevig, Nicolas Regnault

Entanglement in topological phases of matter has so far been investigated through the perspective of their ground-state wave functions. In contrast, we demonstrate that the excitations of fractional quantum Hall (FQH) systems also contain information to identify the system's topological order. Entanglement spectrum of the FQH quasihole (QH) excitations is shown to differentiate between the conformal field theory (CFT) sectors, based on the relative position of the QH with respect to the entanglement cut. For Read-Rezayi model states, as well as Coulomb interaction eigenstates, the counting of the QH entanglement levels in the thermodynamic limit matches exactly the CFT counting, and sector changes occur as non-Abelian quasiholes successively cross the entanglement cut.Entanglement in topological phases of matter has so far been investigated through the perspective of their ground-state wave functions. In contrast, we demonstrate that the excitations of fractional quantum Hall (FQH) systems also contain information to identify the system's topological order. Entanglement spectrum of the FQH quasihole (QH) excitations is shown to differentiate between the conformal field theory (CFT) sectors, based on the relative position of the QH with respect to the entanglement cut. For Read-Rezayi model states, as well as Coulomb interaction eigenstates, the counting of the QH entanglement levels in the thermodynamic limit matches exactly the CFT counting, and sector changes occur as non-Abelian quasiholes successively cross the entanglement cut.

arXiv:1008.5087Physical Review LettersFeb 1, 201150 citations

Partition Functions of Non-Abelian Quantum Hall States

Fisica E Astronomia, Studi Di Firenze

Jan 1, 20100 citations

(k=2,r)

of spinless quantum Hall states, which vanish as

r

powers when

k+1

particles coincide, is generalized to the spinful case. As an application of our method, we show that the counting observed in the particle entanglement spectrum of several spinful states matches the one obtained through the root partitions and our rules. This counting also matches the counting of quasihole states of the corresponding model Hamiltonians, when the latter are available.