The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling $\ensuremath{\nu}=k/(k+2)$. Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted ${\overline{2}}^{k}{1}^{k+1}$ , and show that they lie in the same universality classes as the particle-hole-conjugate RR (``anti-RR'') states. Our analytical results imply that a $[U{(1)}_{k+1}\ifmmode\times\else\texttimes\fi{}U{(2k)}_{\ensuremath{-}1}]/[SU{(k)}_{\ensuremath{-}2}\ifmmode\times\else\texttimes\fi{}U{(1)}_{\ensuremath{-}1}]$ coset conformal field theory describes the edge excitations of the ${\overline{2}}^{k}{1}^{k+1}$ state, suggesting nontrivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence $\overline{n}{\overline{2}}^{2}{1}^{4}$ , with $n=1,2,3$ , to describe the FQH states observed at $\ensuremath{\nu}=2+1/2$, $2+2/5$ , and $2+3/8$ .The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling $\ensuremath{\nu}=k/(k+2)$. Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted ${\overline{2}}^{k}{1}^{k+1}$, and show that they lie in the same universality classes as the particle-hole-conjugate RR (``anti-RR'') states. Our analytical results imply that a $[U{(1)}_{k+1}\ifmmode\times\else\texttimes\fi{}U{(2k)}_{\ensuremath{-}1}]/[SU{(k)}_{\ensuremath{-}2}\ifmmode\times\else\texttimes\fi{}U{(1)}_{\ensuremath{-}1}]$ coset conformal field theory describes the edge excitations of the ${\overline{2}}^{k}{1}^{k+1}$ state, suggesting nontrivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence $\overline{n}{\overline{2}}^{2}{1}^{4}$, with $n=1,2,3$, to describe the FQH states observed at $\ensuremath{\nu}=2+1/2$, $2+2/5$, and $2+3/8$.

arXiv:1902.04173Physical review. B./Physical review. BJun 19, 201946 citations

Parton theory of the fractional quantum Hall effect: New developments

Jainendra Jain

Bulletin of the American Physical SocietyMar 2, 20200 citations

Quasiparticle agglomerates in the Read–Rezayi and anti-Read–Rezayi states

Alessandro Braggio, Dario Ferraro, Nicodemo Magnoli

We calculate the dominant excitations for the $k$ -level ( $k\in\mathbb{N}$ ) Read-Rezayi (RR) states and their particle-hole conjugates, the anti Read-Rezayi ( $\bar{\textrm{RR}}$ ), proposed for quantum Hall states. These states are supposed to be build over the second Landau level with total filling factor $ν=2+ν^*$ with $ν^*=k/(k+2)$ for RR and $ν^*=2/(k+2)$ for $\bar{\textrm{RR}}$ . In the $k$ -level RR states, based on $\mathbb{Z}_k$ parafermions, the dominant excitations are the fundamental quasiparticles with fractional charge $e^*_k= e/(k + 2)$ , with $e$ the electron charge, if $k=2,3$ . For k=4 the single-qp and the 2-agglomerate, with charge $2e^*_k$ , have the same scaling and both dominate, while for $k>4$ the 2-agglomerates are dominant. Anyway the dominance of the 2-agglomerates can be affected by the presence of environmental renormalizations. For all the $k$ -level $\bar{\textrm{RR}}$ states the single-qp and the 2-agglomerate have the same scaling and both dominate. In this case only the presence of environmental renormalizations can make one dominant over the other. We determine the conditions where the environmental renormalizations of the charged and neutral modes make dominant the Abelian 2-agglomerates over the non-Abelian single-quasiparticles in the two models and for any value of $k$ . We conclude observing that, according these predictions, the dominance of 2-agglomerates, at very low energies for the $ν=5/2$ , can be an interesting indication supporting the validity of the anti-Pfaffian model in comparison to the Pfaffian.We calculate the dominant excitations for the $k$-level ($k\in\mathbb{N}$) Read-Rezayi (RR) states and their particle-hole conjugates, the anti Read-Rezayi ($\bar{\textrm{RR}}$), proposed for quantum Hall states. These states are supposed to be build over the second Landau level with total filling factor $ν=2+ν^*$ with $ν^*=k/(k+2)$ for RR and $ν^*=2/(k+2)$ for $\bar{\textrm{RR}}$. In the $k$-level RR states, based on $\mathbb{Z}_k$ parafermions, the dominant excitations are the fundamental quasiparticles with fractional charge $e^*_k= e/(k + 2)$, with $e$ the electron charge, if $k=2,3$. For k=4 the single-qp and the 2-agglomerate, with charge $2e^*_k$, have the same scaling and both dominate, while for $k>4$ the 2-agglomerates are dominant. Anyway the dominance of the 2-agglomerates can be affected by the presence of environmental renormalizations. For all the $k$-level $\bar{\textrm{RR}}$ states the single-qp and the 2-agglomerate have the same scaling and both dominate. In this case only the presence of environmental renormalizations can make one dominant over the other. We determine the conditions where the environmental renormalizations of the charged and neutral modes make dominant the Abelian 2-agglomerates over the non-Abelian single-quasiparticles in the two models and for any value of $k$. We conclude observing that, according these predictions, the dominance of 2-agglomerates, at very low energies for the $ν=5/2$, can be an interesting indication supporting the validity of the anti-Pfaffian model in comparison to the Pfaffian.

arXiv:1207.4604Physica ScriptaNov 1, 20123 citations

New developments in parton theory of the fractional quantum Hall effect

Jainendra Jain

Bulletin of the American Physical SocietyMar 16, 20210 citations

Tripartite composite fermion states

G. J. Sreejith, Ying-Hai Wu, Arkadiusz Wójs +1 more

The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction $\ensuremath{\nu}=2+⅗$, and thereby also its hole conjugate at $2+⅖$ . We study a general class of tripartite composite fermion wave functions, which reduce to the Rezayi-Read ground state and quasiholes for appropriate quantum numbers, but also allow a construction of wave functions for quasiparticles and neutral excitations by analogy to the standard composite fermion theory. We present numerical evidence in finite systems that these trial wave functions capture well the low energy physics of a four-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at $2+⅗$ , and find reasonably good agreement. The ground state as well as several excited states of the four-body interaction are seen to evolve adiabatically into the corresponding Coulomb states for $N=15$ particles. These results support the plausibility of the Read-Rezayi proposal for the $2+⅖$ and $2+⅗$ fractional quantum Hall effect. However, certain other proposals also remain viable, and further study of excitations and edge states will be necessary for a decisive establishment of the physical mechanism of these fractional quantum Hall states.The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction $\ensuremath{\nu}=2+⅗$, and thereby also its hole conjugate at $2+⅖$. We study a general class of tripartite composite fermion wave functions, which reduce to the Rezayi-Read ground state and quasiholes for appropriate quantum numbers, but also allow a construction of wave functions for quasiparticles and neutral excitations by analogy to the standard composite fermion theory. We present numerical evidence in finite systems that these trial wave functions capture well the low energy physics of a four-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at $2+⅗$, and find reasonably good agreement. The ground state as well as several excited states of the four-body interaction are seen to evolve adiabatically into the corresponding Coulomb states for $N=15$ particles. These results support the plausibility of the Read-Rezayi proposal for the $2+⅖$ and $2+⅗$ fractional quantum Hall effect. However, certain other proposals also remain viable, and further study of excitations and edge states will be necessary for a decisive establishment of the physical mechanism of these fractional quantum Hall states.

arXiv:1301.6565Physical Review BJun 24, 201331 citations

The Anatomy of Fractional Quantum Hall States

Nicolas Regnault

Jan 1, 20100 citations

{\overline{2}}^{k}{1}^{k+1}

, and show that they lie in the same universality classes as the particle-hole-conjugate RR (``anti-RR'') states. Our analytical results imply that a $[U{(1)}_{k+1}\ifmmode\times\else\texttimes\fi{}U{(2k)}_{\ensuremath{-}1}]/[SU{(k)}_{\ensuremath{-}2}\ifmmode\times\else\texttimes\fi{}U{(1)}_{\ensuremath{-}1}]$ coset conformal field theory describes the edge excitations of the

{\overline{2}}^{k}{1}^{k+1}

state, suggesting nontrivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence

\overline{n}{\overline{2}}^{2}{1}^{4}

, with

n=1,2,3

, to describe the FQH states observed at $\ensuremath{\nu}=2+1/2$,

2+2/5

, and

2+3/8

We calculate the dominant excitations for the

k

-level (

k\in\mathbb{N}

) Read-Rezayi (RR) states and their particle-hole conjugates, the anti Read-Rezayi (

\bar{\textrm{RR}}

), proposed for quantum Hall states. These states are supposed to be build over the second Landau level with total filling factor

ν=2+ν^*

with

ν^*=k/(k+2)

for RR and

ν^*=2/(k+2)

for

\bar{\textrm{RR}}

. In the

k

-level RR states, based on

\mathbb{Z}_k

parafermions, the dominant excitations are the fundamental quasiparticles with fractional charge

e^*_k= e/(k + 2)

, with

e

the electron charge, if

k=2,3

. For k=4 the single-qp and the 2-agglomerate, with charge

2e^*_k

, have the same scaling and both dominate, while for

k>4

the 2-agglomerates are dominant. Anyway the dominance of the 2-agglomerates can be affected by the presence of environmental renormalizations. For all the

k

-level

\bar{\textrm{RR}}

states the single-qp and the 2-agglomerate have the same scaling and both dominate. In this case only the presence of environmental renormalizations can make one dominant over the other. We determine the conditions where the environmental renormalizations of the charged and neutral modes make dominant the Abelian 2-agglomerates over the non-Abelian single-quasiparticles in the two models and for any value of

k

. We conclude observing that, according these predictions, the dominance of 2-agglomerates, at very low energies for the

ν=5/2

, can be an interesting indication supporting the validity of the anti-Pfaffian model in comparison to the Pfaffian.

The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction $\ensuremath{\nu}=2+⅗$, and thereby also its hole conjugate at

2+⅖

. We study a general class of tripartite composite fermion wave functions, which reduce to the Rezayi-Read ground state and quasiholes for appropriate quantum numbers, but also allow a construction of wave functions for quasiparticles and neutral excitations by analogy to the standard composite fermion theory. We present numerical evidence in finite systems that these trial wave functions capture well the low energy physics of a four-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at

2+⅗

, and find reasonably good agreement. The ground state as well as several excited states of the four-body interaction are seen to evolve adiabatically into the corresponding Coulomb states for

N=15

particles. These results support the plausibility of the Read-Rezayi proposal for the

2+⅖

and

2+⅗

fractional quantum Hall effect. However, certain other proposals also remain viable, and further study of excitations and edge states will be necessary for a decisive establishment of the physical mechanism of these fractional quantum Hall states.