Berlin 2024 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 5: Machine Learning in Dynamics and Statistical Physics I

DY 5.10: Vortrag

Montag, 18. März 2024, 12:00–12:15, BH-N 243

Mean-field theories are simple for neural quantum states — •Fabian Ballar Trigueros, Tiago Mendes-Santos, and Markus Heyl — Universität Augsburg

The utilization of artificial neural networks for representing quantum many-body wave functions has garnered significant attention, however, quantifying state complexity within this neural quantum states framework remains elusive. In this study, we address this key open question from the complementary point of view: Which states are simple to represent with neural quantum states? Concretely, we show on a general level that ground states of mean-field theories with permutation symmetry only require a limited number of independent neural network parameters. We analytically establish that, in the thermodynamic limit, convergence to the ground state of the fully-connected transverse-field Ising model (TFIM), the mean-field Ising model, can be achieved with just one single parameter. Expanding our analysis, we explore the behavior of the 1-parameter ansatz under breaking of the permutation symmetry. For that purpose, we consider the TFIM with tunable long-range interactions, characterized by an interaction exponent α. We show analytically that the 1-parameter ansatz for the neural quantum state still accurately captures the ground state for a whole range of values for 0≤ α ≤ 1, implying a mean-field description of the model in this regime. We also comment on a potential method to identify and extract information from the neural network weight matrix that can give insight into the complexity of the state representation.

Keywords: Neural quantum states; quantum complexity; machine learning; long-range models