Probing Critical Behavior Near the Phase Transitions of Correlated Systems via Variational Diagrammatic Monte Carlo Built on DMFT

We develop a variational perturbation expansion around dynamical mean-field theory (DMFT) that systematically incorporates nonlocal correlations beyond the local correlations treated by DMFT. Starting from the DMFT solution with a variationally controlled order parameter, our approach predicts the Néel temperature across a wide range of interaction strengths while maintaining low computational cost. Various observables can also be extracted from the convergence behavior of this variational perturbation expansion. In the three-dimensional cubic Hubbard model, we apply this approach to investigate how the DMFT Néel temperature is suppressed from its mean-field value, and how the critical behavior near the finite-temperature phase transition evolves from the mean-field to the Heisenberg universality class.