Berlin 2018 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 63: Topology: Quantum Hall Systems
TT 63.6: Vortrag
Mittwoch, 14. März 2018, 16:15–16:30, A 053
Chiral Topological Phases from Artificial Neural Networks — Raphael Kaubruegger1,3, •Lorenzo Pastori1,2, and Jan Carl Budich1,2 — 1Department of Physics, University of Gothenburg, SE 412 96 Gothenburg, Sweden — 2Institute of Theoretical Physics, Technische Universitaet Dresden, 01062 Dresden, Germany — 3Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
Motivated by recent progress in applying techniques from the field of artificial neural networks (ANNs) to quantum many-body physics, we investigate as to what extent the flexibility of ANNs can be used to efficiently study systems that host chiral topological phases such as fractional quantum Hall (FQH) phases. With benchmark examples, we demonstrate that training ANNs of restricted Boltzmann machine type in the framework of variational Monte Carlo can numerically solve FQH problems to good approximation. Furthermore, we show by explicit construction how n-body correlations can be kept at an exact level with ANN wave-functions exhibiting polynomial scaling with power n in system size. Using this construction, we analytically represent the paradigmatic Laughlin wave-function as an ANN state.