2009/01/14 by Nicolas Regnault, N. Regnault, B. Andrei Bernevig +1 · 128 citations
Computer Science · Mathematics · Physics and Astronomy · #Boson #Coulomb #Ground state #Hamiltonian (control theory) #Mathematical physics #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.103.016801
published in Physical Review Letters 103(1), 016801 (American Physical Society) · 7 pages, 8 figures
arxiv created 2009/01/14 · openalex publication_date 2009/06/29 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We obtain several clustering properties of the Jain states at filling k/2k+1: they are a product of a Vandermonde determinant and a bosonic polynomial at filling k/k+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 nu=2/5 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.