Speaker
Description
Nonequilibrium Green's function (NEGF) simulations face a steep growth of memory and computational cost with the number of time steps. Tensor networks offer a general solution: the quantics tensor train (QTT) representation compresses multi-time correlation functions by exploiting scale separation, and tensor cross interpolation (TCI) learns compressed tensor-train representations of functions and high-dimensional integrands from a small number of samples. In this talk, I give a pedagogical introduction to QTT and TCI: what they are, when and why they work, and how they can be used in practice through the open-source tensor4all ecosystem [1]. I briefly illustrate their potential with recent applications, including memory-efficient Kadanoff-Baym and GW simulations [2,3], a causality-based divide-and-conquer Dyson solver [4], weak-coupling TCI impurity solvers for equilibrium and nonequilibrium dynamical mean-field theory [5,6], and nonequilibrium two-particle correlation functions within a generalized Keldysh formalism [7]. Finally, I present tensor4all-rs, a new Rust-based library that unifies these tools, developed with systematic use of agentic coding and designed for HPC applications.
[1] Y. Núñez Fernández et al., SciPost Phys. 18, 104 (2025).
[2] M. Murray, H. Shinaoka, and P. Werner, Phys. Rev. B 109, 165135 (2024).
[3] M. Środa, K. Inayoshi, H. Shinaoka, and P. Werner, Phys. Rev. Lett. (2025), arXiv:2412.14032.
[4] K. Inayoshi, M. Środa, A. Kauch, P. Werner, and H. Shinaoka, SciPost Phys. 20, 077 (2026).
[5] S. Matsuura, H. Shinaoka, P. Werner, and N. Tsuji, Phys. Rev. B 111, 155150 (2025).
[6] S. Matsuura, H. Shinaoka, P. Werner, and N. Tsuji, arXiv:2607.00702.
[7] K. Inayoshi, H. Shinaoka, and Y. Murakami, arXiv:2607.11055.