Variational Discrete Action Theory

Abstract: Here we propose the Variational Discrete Action Theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathcal{N}$, which monotonically approaches the exact solution with increasing $\mathcal{N}$. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green's function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model (AIM) and the $d=\infty$ Hubbard model. For the latter, we evaluate $\mathcal{N}=2-4$, where $\mathcal{N}=2$ recovers the Gutzwiller approximation (GA), and we show that $\mathcal{N}=3$, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.