Variational Discrete Action Theory

TL;DR

The paper introduces Variational Discrete Action Theory (VDAT), a new variational approach for analyzing quantum many-body Hamiltonians that improves accuracy with increasing complexity and unifies various existing methods.

Contribution

VDAT provides a novel variational framework using a sequential product density matrix ansatz, enabling exact evaluation in key models and capturing Mott physics efficiently.

Findings

VDAT exactly evaluates the SPD in the Anderson impurity model and the Hubbard model.

At N=2, VDAT recovers the Gutzwiller approximation; at N=3, it captures Gutzwiller-Baeriswyl wave function.

VDAT offers a flexible, competitive approach for studying quantum Hamiltonians.

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.