Berlin 2018 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 91: Correlated Electrons: Method Development

TT 91.7: Vortrag

Donnerstag, 15. März 2018, 16:30–16:45, H 0104

Fractional quantum Hall effect in the interacting Hofstadter model via tensor networksMatthias Gerster1, •Matteo Rizzi2, Pietro Silvi1,3, Marcello Dalmonte4, and Simone Montangero1,5,61ICQS & IQST, Ulm University, Germany — 2Institut für Physik, Johannes Gutenberg-Universität, Mainz, Germany — 3Institute for Theoretical Physics, University of Innsbruck, Austria — 4Abdus Salam ICTP, Trieste, Italy — 5Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany — 6Dipartimento di Fisica e Astronomia, Università di Padova, Italy

We show via tensor network methods that the Harper-Hofstadter Hamiltonian for hard-core bosons on a square geometry supports a topological phase realizing the ν − 1/2 fractional quantum Hall (FQH) effect on the lattice. We address the robustness of the ground-state degeneracy and of the energy gap, measure the many-body Chern number, and characterize the system using Green functions, showing that they decay algebraically at the edges of open geometries, indicating the presence of gapless edge modes. Moreover, we estimate the topological entanglement entropy by taking a combination of lattice bipartitions that reproduces the topological structure of the original proposals by Kitaev and Preskill, and Levin and Wen. The numerical results show that the topological contribution is compatible with the expected value γ=1/2. Our results provide extensive evidence that FQH states are within reach of state-of-the-art cold-atom experiments.
Gerster et al., Phys. Rev. B 96, 195123 (2017)

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