Freiburg 2024 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 42: Long-range Interactions
Q 42.2: Vortrag
Donnerstag, 14. März 2024, 11:30–11:45, HS 1015
Neural Network Quantum States for the Hofstadter Model with Higher Local Occupations and Long-Range Interactions — •Fabian Döschl1,2, Felix Palm1,2, Hannah Lange1,2,3, Fabian Grusdt1,2, and Annabelle Bohrdt2,4 — 1Ludwig-Maximilians-University Munich — 2Munich Center for Quantum Science and Technology — 3Max-Planck-Institute for Quantum Optics — 4University of Regensburg
Neural network quantum states (NQS) have gained significant interest in current research due to their immense representative power. In this study, we show that RNN wave functions can be employed to study systems relevant to current research in quantum many body physics. Specifically, we employ a 2D tensorized gated RNN to explore the Hofstadter Hamiltonian with a variable local Hilbert space cut off. We benchmark the NQS against exact diagonalization for the Hofstadter Hamiltonian with on site interactions on a 6×6 square lattice. Remarkably, this method is capable of effectively identifying and representing the ground state. A further benchmark against DMRG for 12×12 systems will reveal phases that are hard to simulate with the RNN-NQS ansatz. Moreover, we demonstrate that NQSs are capable of capturing interactions over large distances, a task that is far from being solved by current methods. This technique is applied to a Hofstadter Hamiltonian with long-range interactions on a 12×12 square lattice. This work aims to enhance our understanding of representing strongly correlated quantum systems with NQS.
Keywords: Neural Quantum States; Machine Learning; Simulation of FQH systems