2021/08/31 by Kiryl Pakrouski · 7 citations
Mathematics · Physics and Astronomy · #Combinatorics #Coulomb #Electron #Fermion #Hamiltonian (control theory) #Mathematical physics #Mathematics #Pfaffian #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum mechanics #Quantum, superfluid, helium dynamics #Wave function #cond-mat.mes-hall #cond-mat.str-el #quant-ph
paper · pdf · open access · doi:10.1103/physrevb.104.245306
published in Physical review. B./Physical review. B 104(24) (American Physical Society) · v3: journal version. Added various definitions to make the paper self-contained. Improved presentation incl. clearer plots
openalex publication_date 2021/12/29 · arxiv created 2022/01/04 · arxiv updated 2022/01/05 · openalex created_date 2022/02/08 · openalex updated_date 2026/08/06
We present two two-body Hamiltonians that approximate the exact particle-hole Pfaffian wave function with their ground states for all the system sizes where this wave function has been numerically constructed to date. The approximate wave functions have high overlap with the original and reproduce well the low-lying entanglement spectrum and structure factor. The approximate generating Hamiltonians are obtained by an optimization procedure where three to four pseudopotentials are varied in the neighbourhood of second Landau level Coulomb interaction or of a noninteracting model. They belong to a finite region in the variational space of Hamiltonians where each point approximately generates the particle-hole Pfaffian. We diagonalize the identified Hamiltonians for up to 20 electrons and find that for them the particle-hole Pfaffian shift appears energetically more favorable. The possibility to interpret the data in terms of composite fermions is discussed.