Regensburg 2025 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 20: Many-body Quantum Dynamics II (joint session DY/TT)

DY 20.12: Vortrag

Mittwoch, 19. März 2025, 12:30–12:45, H37

Machine learning approach to study the properties of ground and excited states in the 1D Bose-Hubbard model — •Yilun Gao¹, Alberto Rodríguez González^2,3, and Rudolf A. Römer¹ — ¹Department of Physics, University of Warwick, Coventry, CV4 7AL — ²Departamento de Física Fundamental, Universidad de Salamanca, E-37008 Salamanca, Spain — ³Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, E-37008 Salamanca, Spain

Many-body quantum interacting systems continue to play a key role in theoretical developments of modern condensed matter physics. Various numerical techniques have been used to explore the features of these many-body systems. Exact diagonalization methods, which most results going beyond ground state properties are based on, can only deal with small system sizes L 15 because the Hilbert dimensions grow exponentially in L. Recently, deep learning has emerged as a numerical technique that uses strategies of artificial intelligence to predict the physics of such systems. Here we focus on the Bose-Hubbard chain and use HubbardNet [1] to investigate the physics of ground and excited states. We show that the energies and wavefunctions predicted by HubbardNet agree well with the ones calculated by exact diagonalization over a broad range of interaction strengths. We investigate the properties of the eigenstates via their finite-size generalized fractal dimensions. [1] Ziyan Zhu, et al., HubbardNet: Efficient predictions of the Bose-Hubbard model spectrum with deep neural networks, Phys. Rev. Res., 5, 043084 (2023)

Keywords: HubbardNet; Machine learning; Bose-Hubbard model; deep neural networks