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Bulletin of the American Physical Society

High-Order Renormalized Perturbative Approach for Strongly-Correlated Fermions

Riccardo Rossi, Fedor Šimkovic, Gabriele La Spada, Renaud Garioud, Kris Van Houcke, Michel Ferrero, Félix Werner

Published Mar 16, 2021• 0 citations
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We present a microscopic examination for the itinerant-localized duality model which has been proposed to understand anomalous properties of strongly correlated systems like the heavy fermions by Kuramoto and Miyake, and also useful to describe the anomalous properties of the high-Tc cupurates. We show that the thermodynamic potential of the strongly interacting Hubbard model can be rearranged in the form of duality model on the basis of renormalized perturbation expansion of the Luttinger-Ward functional if the one-particle spectral weight exhibits triple peak structure. We also examine the incoherent degrees of freedom described as a ``localized spin'' and show on the basis of the pertubation expansion that there exists commensurate superexchange-type interaction among the ``localized spins''.
The unusual low temperature behaviour of metals and metal alloys, such as heavy fermion systems, Mott insulators and unconventional superconductors, has been a central topic of scientific investigation for over half a century. Due to strong correlations between the many particles, the solution to most theoretical models of these systems is difficult because standard perturbation methods break down. In certain cases, non-perturbative renormalization group approaches can be used to access the low energy behaviour and take into account the effects of strong correlations. However, these methods do not work for several important and interesting classes of model. These include lattice models with finite dimension, models with impurities of high degeneracy and steady state transport through quantum dots. The aim of this thesis is therefore to develop a new and general renormalization group approach that will lend itself to wide application in models where existing techniques fail. The method explored here utilises renormalized perturbation theory (RPT) in conjunction with scaling equations and collective excitations. It is tested on the single impurity Anderson model, the paradigmatic model used to understand magnetic impurities within a non-magnetic host metal. The Anderson model is simple yet exhibits interesting features due to strong correlation, such as a single renormalized low energy scale called the Kondo temperature. This model is also well understood as it has been solved using the numerical renormalization group (NRG), which provides ample numerical data against which this new technique is compared. Finally, a preliminary study is given for this method when it is applied to a wider class of models.
The strongly contracted variant of second-order N-electron valence state perturbation theory (NEVPT2) is an efficient perturbative method to treat dynamic correlation without the problems of intruder states or level shifts, while the density matrix renormalization group (DMRG) provides the capability to address static correlation in large active spaces. We present a combination of the DMRG and strongly contracted NEVPT2 (DMRG-SC-NEVPT2) that uses an efficient algorithm to compute high-order reduced-density matrices from DMRG wave functions. The capabilities of DMRG-SC-NEVPT2 are demonstrated on calculations of the chromium dimer potential energy curve at the basis set limit, and the excitation energies of a trimer model of poly(p-phenylenevinylene) (PPV(n = 3)).