2015/06/30 by Ivan Dario Jimenez Rodriguez, Ivan D. Rodriguez, Anne E. B. Nielsen · 13 citations
Mathematics · Physics and Astronomy · #Conformal field theory #Conformal map #Fractional quantum Hall effect #Ground state #Hamiltonian (control theory) #Lattice (music) #Magnetic field #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Theoretical physics #Topological Materials and Phenomena #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.92.125105
published in Physical Review B 92(12) (American Physical Society) · 8 pages, 7 figures; v2: minor changes and accepted for publication in Phys. Rev. B
arxiv created 2015/08/20 · openalex publication_date 2015/09/02 · arxiv updated 2015/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
There has been significant interest in recent years in finding fractional quantum Hall physics in lattice models, but it is not always clear how these models connect to the corresponding models in continuum systems. Here we introduce a family of models that is able to interpolate between a recently proposed set of lattice models with Laughlin-like ground states constructed from conformal field theory and models with ground states that are practically the usual bosonic/fermionic Laughlin states in the continuum. Both the ground state and the Hamiltonian are known analytically, and we find that the Hamiltonian in the continuum limit does not coincide with the usual delta interaction Hamiltonian for the Laughlin states. We introduce quasiholes into the models and show analytically that their braiding properties are as expected if the quasiholes are screened. We demonstrate screening numerically for the 1/3 Laughlin model and find that the quasiholes are slightly smaller in the continuum than in the lattice. Finally, we compute the effective magnetic field felt by the quasiholes and show that it is close to uniform when approaching the continuum limit. The techniques presented here to interpolate between the lattice and the continuum can also be applied to other fractional quantum Hall states that are constructed from conformal field theory.