Speaker
Description
In this work, we extend the normalizing-flow-based generalized density-of-states (NF-gDoS) method to the doped Hubbard model. The Hubbard model is known to exhibit a sign problem in the presence of a chemical potential. The NF-gDoS framework is attractive because it reformulates the original complex-weight sampling problem by separating the complex phase from the Boltzmann distribution and encoding it instead in a one-dimensional oscillatory integral.
Recent studies have demonstrated that the NF-gDoS method can successfully reconstruct the partition function in 1+1D scalar field theory, correctly reproducing the Lee–Yang zeros. In a separate study of 1+1D U(1) gauge theory with a $\theta$-term, it was shown that the density of states can be qualitatively reconstructed, highlighting the importance of expressive normalizing flows.
Building on these results, we apply expressive conditional-normalizing-flow (CNF) architectures to the doped Hubbard model and systematically benchmark the resulting density of states against exact results for small system sizes. Our study provides a first assessment of the applicability of CNF-gDoS to a strongly correlated fermionic system. We identify key challenges, including limitations related to model expressivity and stability, and outline possible directions for improving the robustness of the approach in more demanding regimes.