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.

arXiv comment5 pages, 2 figures

References in corpus (17)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Towards Practical Quantum Variational Algorithms
• Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials
• From density-matrix renormalization group to matrix product states
• Energy resolution and discretization artefacts in the numerical renormalization group
• Variational description of Mott insulators
• LDA+Gutzwiller Method for Correlated Electron Systems: Formalism and Its Applications
• Hund's metal physics: from SrNiO${}_2$ to NdNiO${}_2$
• Multiorbital processes rule the Nd${}_{1-x}$Sr${}_x$NiO${}_2$ normal state
• Kondo screening cloud in the single-impurity Anderson model: A density matrix renormalization group study
• Sr${}_2$MoO${}_4$ and Sr${}_2$RuO${}_4$: Disentangling the Roles of Hund's and van Hove Physics
• Foundations of the Variational Discrete Action Theory
• Ground-state properties of the symmetric single-impurity Anderson model on a ring from Density-Matrix Renormalization Group, Hartree-Fock, and Gutzwiller theory
• Off-shell effective energy theory: a unified treatment of the Hubbard model from d=1 to d=$\infty$

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