Group seminar at MPQ and Zoom: Tensor Network Study and AI-driven Analysis of the $t$-$t'$ Fermi-Hubbard Model

Changkai Zhang LMU Munich, Germany
Group seminar at MPQ lecture hall and Zoom
Thursday, 29 January, 09:00am (MEZ)

Tensor-network methods are among the most powerful contemporary solvers for strongly correlated quantum many-body systems, providing high-accuracy benchmarks for fermionic systems such as the doped Fermi-Hubbard model, which remains notoriously challenging for Monte Carlo approaches. In this talk, I will present a comprehensive study of the $t$-$t'$ Fermi-Hubbard model combining state-of-the-art iPEPS (for zero-$T$) with XTRG (for finite-$T$) tensor networks, together with an AI-driven thermometer for ultracold-atom quantum simulators.
iPEPS directly targets 2D ground states in the thermodynamic limit, enabling a controlled analysis of competing orders. Using this approach, we address the long-standing debate over the existence and properties of the superconducting orders in the doped Hubbard model, highlight the impact of $t'$, and extract insights into candidate pairing mechanisms. Complementarily, XTRG cools the system exponentially fast in inverse temperature, allowing us to map thermodynamic observables across a broad temperature window and to partially bridge to the iPEPS ground states. This yields a comprehensive snapshot dataset spanning multiple temperature scales, providing a foundation for training a novel AI model that captures the underlying correlation structure. We demonstrate that this AI system functions as an accurate thermometer, inferring temperature from correlation features in experimentally accessible ensembles of snapshots.