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DY: Fachverband Dynamik und Statistische Physik
DY 25: Many-Body Quantum Dynamics (joint session DY/TT)
DY 25.11: Talk
Wednesday, March 29, 2023, 12:30–12:45, MOL 213
Fast Time-Evolution of Matrix-Product States using the QR decomposition — •Jakob Unfried1,2, Johannes Hauschild1, and Frank Pollmann1,2 — 1Department of Physics, TFK, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany — 2Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany
Numerical simulations of quantum many-body dynamics in and out of equilibrium is essential for the understanding of a wide range of physical phenomena. Efficient matrix product state simulation techniques, such as time evolution block decimation (TEBD), are widely successful in extracting experimentally relevant signatures, such as dynamical correlation functions. We propose and benchmark a modified TEBD algorithm that uses a truncation scheme based on the QR decomposition instead of the singular value decomposition (SVD). The modification reduces the scaling with the dimension of the physical Hilbert space d from d3 down to d2. Unlike the SVD, the QR decomposition allows for highly efficient implementations on GPU hardware. In a benchmark simulation of a global quench in a quantum clock model, we observe a speedup of orders of magnitude comparing the QR based scheme on a GPU to the SVD based TEBD on CPU.