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%0 Thesis %A Passetti, Giacomo %T Emerging numerical techniques for the study of entangled quantum many-body systems %I RWTH Aachen University %V Dissertation %C Aachen %M RWTH-2024-00166 %P 1 Online-Ressource : Illustrationen %D 2023 %Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2024 %Z Dissertation, RWTH Aachen University, 2023 %X We study numerical techniques for the representation of many-body quantum wave functions. Advancements in this thesis involve two different main topics: (i) Fundamental conditions for the formation of light-matter entanglement, studied applying the established density matrix renormalization group approach. (ii) A systematic study of deep feed forward neural networks, where we investigate their capabilities in the representation of physically relevant quantum states characterized by volume law entanglement, and their entanglement properties in correspondence of a critical phase transition. In the first part of this thesis, we introduce a tight binding model for a non-interacting 1D fermionic chain, coupled to the single resonant mode of a cavity setup. We show that this model is exactly solved considering a tensor product wave function that disentangles the fermionic from the photonic degrees of freedom. Including also fermion-fermion interactions, we consider both an analytic high frequency expansion, and a numerical approach based on the density matrix renormalization group. We show that with few assumptions on the specific interaction form considered, it is possible to identify a relation between the fluctuations of the current operator and the light-matter entanglement entropy from the analytic expansion. The numerical study confirms the results in the high frequency limit, and shows that the qualitative picture holds also when finite frequencies are considered. In the second part of this thesis, we consider deep feed forward neural networks formulated as neural quantum states. We are interested in studying whether this class of variational ansätze wave functions can be successfully adopted to represent the ground state of the Sachdev-Ye-Kitaev model. We show that using several training schemes, the number of network free parameters required to learn the Sachdev-Ye-Kitaev model ground state scales exponentially with the physical system size considered. This result is robust against different variations on the network architecture implemented, implying that this variational ansatz doesn't outperform exact diagonalization in the solution of the problem. Finally, we study deep feed forward neural networks initialized with random weights. We show that a critical transition from ordered to chaotic phase already known in literature, maps to critical behavior of the bipartite entanglement entropy of the neural quantum state represented by the network. We show a correspondence between the deep neural network characteristic length for the correlation propagation across the layers, and the bipartite entanglement entropy. We identify two different entanglement scaling behavior in the two network phases, and we show that this affects also the behavior of physical observables. %F PUB:(DE-HGF)11 %9 Dissertation / PhD Thesis %R 10.18154/RWTH-2024-00166 %U https://publications.rwth-aachen.de/record/976352