Topological Entanglement and Clustering of Jain Hierarchy States

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Abstract

We obtain several clustering properties of the Jain states at filling k2k+1: they are a product of a Vandermonde determinant and a bosonic polynomial at filling kk+1 which vanishes when k+1 particles cluster together. We show that all Jain states satisfy a "squeezing rule" which severely reduces the dimension of the Hilbert space necessary to generate them. We compute the topological entanglement spectrum of the Jain ν=25 state and compare it to both the Coulomb ground state and the nonunitary Gaffnian state. All three states have a very similar "low-energy" structure. However, the Jain state entanglement "edge" state counting matches both the Coulomb counting as well as two decoupled U(1) free bosons, whereas the Gaffnian edge counting misses some of the edge states of the Coulomb spectrum.

Original languageEnglish (US)
Article number016801
JournalPhysical review letters
Volume103
Issue number1
DOIs
StatePublished - Jun 29 2009

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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