Efficient Auxiliary Bath Approximations of Gaussian Fermionic Influence Functionals

Diplôme Thèse Efficient Auxiliary Bath Approximations of Gaussian Fermionic Influence Functionals eng 2025-04-29 2025-04-29 author Thoenniss Julian 946499 director Giamarchi Thierry 134665 Département de physique de la matière quantique (FIMAC) director Abanin Dmitry 842597 10.13097/archive-ouverte/unige:185106 urn:nbn:ch:unige-1851065 Sc. 5902 This thesis introduces efficient approximation techniques for fermionic Gaussian influence functionals (IFs) to simulate the dynamics of quantum impurity systems coupled to non-interacting baths. The IF encapsulates the memory effects induced by the bath on the impurity, obtained by integrating out the bath degrees of freedom within the path integral formalism. The central contribution of this work is the development of auxiliary baths that faithfully reproduce these memory effects while significantly reducing bath complexity with controlled accuracy. Two complementary approaches are introduced: (i) A framework is developed to represent the IF as a Matrix Product State (MPS) in the temporal domain, enabling efficient computation of impurity dynamics through tensor contractions. (ii) Alternatively, a time-local description is achieved by approximating the bath hybridization function---the key determinant of the IF---as a sum of decaying exponentials. This pseudomode approach offers an intuitive mapping to an effective Lindblad equation, where the impurity interacts with a finite set of auxiliary modes that faithfully reproduce the original bath’s influence. These approaches bridge path integral techniques with master equation formalisms and modern tensor network methods, providing both conceptual clarity and computational efficiency. The thesis presents results on error bounds and computational complexity, alongside applications to nonequilibrium impurity problems, including quantum quenches and relaxation dynamics, demonstrating the versatility and robustness of the proposed methods. Dewey 500.2 37 Département de physique théorique 133 false 967 Groupe Abanin 780 Groupe Giamarchi 93137b41-db30-425c-8dae-60bbbe4fdf7d Thesis Public Thoenniss_these_publiee.pdf 26885327 application/pdf d5411e6e146b79372dc42697deadf051150c70dfb6a322c6040456b4ad5dcd46 4b7e0135-339a-477c-a2ef-c4e1f52bd05d Imprimatur Public imprimatur.pdf 312334 application/pdf 09e4561bdd977545b484d03c33015fe515f89b0c8ed785a1be0edd883322754b Vignette Public setup_paper-1.png 288893 image/png openAccess Faculté des sciences / Section de physique / Département de physique théorique

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