A new version of the time-dependent variational principle for neural quantum states

• Applicant: Professor Dr. Markus Philip Ludwig Heyl
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 530080784

It is the central goal of this proposed research project to advance the theoretical description of the nonequilibrium dynamics of interacting quantum matter. The remarkable advancements in quantum simulators within the last two decades have brought about a revolution in experimentally generating, manipulating, and probing quantum many-body states. These developments have created the experimental basis to explore uncharted physical phenomena and novel dynamical paradigms. In the past few years, further fascinating possibilities have been emerging on the experimental side due to the impressive progress in Rydberg tweezer arrays providing an experimental platform for the exploration of quantum spin models in fully tunable geometries. However, the theoretical description of the dynamics in interacting quantum many-body systems in two dimensions is facing key challenges, in particular when it comes to numerically exact approaches. In recent years the neural quantum state approach has emerged as a promising alternative for solving the quantum many-body problem. Within the neural quantum states method the quantum many-body wave function is encoded into an artificial neural network, thereby attempting to capitalize on the overwhelming success of machine learning methods in computer science for advancing quantum physics. As of late remarkable developments have highlighted the impressive capabilities of this approach both concerning the calculation of ground states and real-time dynamics. Importantly, however, the neural quantum states approach for dynamics is facing still severe limitations leading to numerical instabilities which are still awaiting a resolution in order to make neural quantum states a universally applicable method. It will be the key goal of this proposed research project to formulate a new version of the time-dependent variational principle, which underlies the solution of the dynamics for neural quantum states. In this way we aim to combine the expressive power of artificial neural networks with the numerical stability of a different method called variational classical networks, which constitute an alternative method to solve for dynamics in quantum matter. Based on these methodological advances it will be the central scope of the proposed research project to explore so far inaccessible physical phenomena beyond one spatial dimension. Specifically, we will target the dynamics of the roughening transition in the paradigmatic quantum Ising model on the square lattice and the quantum Kibble-Zurek mechanism in three spatial dimensions. We expect that this methodological development will push the neural quantum state approach to the next level allowing us to solve for the dynamics of interacting quantum matter beyond one dimension in regimes which have so far been inaccessible by state-of-the-art numerical approaches.

• DFG Programme: Research Grants