Regensburg 2022 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 21: Correlated Electrons: Poster Session
TT 21.32: Poster
Mittwoch, 7. September 2022, 15:00–18:00, P1
Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces at the example of the Holstein model — •Thomas Köhler1, Jan Stolpp2, and Sebastian Paeckel3 — 1Uppsala University, Sweden — 2Georg-August-Universität Göttingen, Germany — 3University of Munich, Germany
Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become a successful tool to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. Based on an intimate connection between the Schmidt values of the corresponding matrix-product-state representation and the single-site reduced density matrix, this allows for an efficient treatment of systems with large local dimensions. We demonstrate this new mapping, provide an implementation recipe, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L = 501 while accounting for Nph = 63 phonons per site with high precision in the CDW phase.