Regensburg 2025 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 2: Nonequilibrium Quantum Systems (joint session TT/DY)
DY 2.1: Vortrag
Montag, 17. März 2025, 09:30–09:45, H31
Solving the nonequilibrium Dyson equation with quantics tensor trains — •Ken Inayoshi1, Maksymilian Środa2, Anna Kauch3, Philipp Werner2, and Hiroshi Shinaoka1 — 1Department of Physics, Saitama University, Saitama, Japan — 2Department of Physics, University of Fribourg, Fribourg, Switzerland — 3Institute of Solid State Physics, TU Wien, Vienna, Austria
The nonequilibrium Green’s function (NEGF) method is a powerful tool to investigate dynamical phenomena in quantum many-body systems. However, the time-translational symmetry breaking of Green’s functions (GFs) makes the simulation of long-time dynamics computationally and memory-intensive. To overcome these, various memory compression techniques have been proposed for the NEGF method [1,2]. Among these, quantics tensor trains (QTT) have been attracting a focus for its ability to exponentially compress the data size of GFs [3]. While a prototype NEGF method with QTT has been developed [4], its benchmarks were limited to the short-time dynamics due to technical challenges such as the slow convergence of self-consistent calculations. We propose an improved implementation to reach the longer time regions, using a variational method for solving the Dyson equation and a causality-based divide-and-conquer algorithm [5,6]. In this contribution, we benchmark our method in relevant test cases [6].
[1] J. Kaye and D. Golež, SciPost Phys. 10, 091 (2021).
[2] M. Eckstein, arXiv:2410.19707.
[3] H. Shinaoka et al., Phys. Rev. X 13, 021015 (2023).
[4] M. Murray et al., Phys. Rev. B 109, 165135 (2024).
[5] M. Środa et al., in preparation
[6] K. Inayoshi et al., in preparation
Keywords: Nonequilibrium quantum many-body physics; Nonequilibrium Green's function method; Tensor network; Quantics tensor trains