Strong parameter renormalization from optimum lattice model orbitals

Abstract

We revisit the old problem of which is the best single particle basis to express a Hubbard-like lattice model. A rigorous variational solution of this problem leads to equations in which the answer depends in a self-consistent manner on the solution of the lattice model itself. Contrary to naive expectations, for arbitrary small interactions, the optimized orbitals differ from the non-interacting ones, leading also to substantial changes in the model parameters as shown analytically and in an explicit numerical solution for a simple double-well one-dimensional case. At strong coupling, we obtain the direct exchange interaction with a very large renormalization with important consequences for the explanation of ferromagnetism with model hamiltonians. Moreover, in the case of two atoms and two fermions we show that the optimization equations are closely related to reduced density matrix functional theory thus establishing an unsuspected correspondence between continuum and lattice approaches.

11 pages, 2 figures

References in corpus (27)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Maximally localized Wannier functions: Theory and applications
• Supersymmetry and Quantum Mechanics
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Ab initio calculations of quasiparticle band structure in correlated systems: LDA++ approach
• First-principles Calculations of the Electronic Structure and Spectra of Strongly Correlated Systems: Dynamical Mean-field Theory
• A natural orbital functional for the many-electron problem
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Reduced Density Matrix Functional for Many-Electron Systems
• LDA+Gutzwiller Method for Correlated Electron Systems: Formalism and Its Applications
• Density-Matrix-Power Functional: Performance for Finite Systems and the Homogeneous Electron Gas
• Exact Kohn-Sham potential of strongly correlated finite systems
• Spectral density and metal-insulator phase transition in Mott insulators within RDMFT
• Gutzwiller density functional theory for correlated electron systems
• Ground-state phase diagram of the quantum Rabi model
• Many-body models for molecular nanomagnets
• Discontinuity of the chemical potential in reduced-density-matrix-functional theory
• Phase Diagram of Na${}_x$CoO${}_2$ Studied by Gutzwiller Density Functional Theory
• No-go theorem for the description of Mott phenomena with conventional Density Functional Theory methods
• Gutzwiller Density Functional Theory: a formal derivation and application to ferromagnetic nickel
• Mean photon number dependent variational method to the Rabi model
• Extended Hubbard model with renormalized Wannier wave functions in the correlated state III: Statistically consistent Gutzwiller approximation and the metallization of atomic solid hydrogen
• Ab-initio Gutzwiller method: first application to Plutonium
• Extended Hubbard model with renormalized Wannier wave functions in the correlated state: beyond the parametrized models
• Density functional theory with adaptive pair density
• Construction of Localized Basis for Dynamical Mean Field Theory