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Theoretical Chemistry Accounts

Electron sharing and localization in real space for the Mott transition from 1RDMFT periodic calculations

A. I. Baranov, Ángel Martín Pendás

Published Aug 9, 2017• 0 citations
Publisher

Abstract

One-particle reduced density matrix functional theory (1RDMFT) has been applied for the investigation of the real-space picture of the Mott transitions in archetypal hydrogen lattices. The evolution of the degree of electron localization during the transition has been evaluated using electron sharing indices for QTAIM atoms, and the connection between the strength of electronic correlation expressed by the 1RDMFT correlation energy and the degree of electron localization has been analyzed at various stages of transition. The spatial decay of the electron sharing indices in the course of transition has also been evaluated and compared with the results obtained for the Hubbard model and finite cluster calculations.

DOI
10.1007/s00214-017-2125-8

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One-particle reduced density matrix functional theory (1RDMFT) has been applied for the investigation of the real-space picture of the Mott transitions in archetypal hydrogen lattices. The evolution of the degree of electron localization during the transition has been evaluated using electron sharing indices for QTAIM atoms, and the connection between the strength of electronic correlation expressed by the 1RDMFT correlation energy and the degree of electron localization has been analyzed at various stages of transition. The spatial decay of the electron sharing indices in the course of transition has also been evaluated and compared with the results obtained for the Hubbard model and finite cluster calculations.
We study in this contribution the spatial decay rate of real-space localization and delocalization indices in correlated systems. To that end, we examine Hubbard and quantum chemical models of simple cyclic hydrogen chains, showing that all descriptors of delocalization converge quickly toward the infinite chain limits. It is then shown that the localization index may be understood as a generalization of the standard order parameter in Mott insulator transitions and that the origin of the enigmatic sigmoidal profile of delocalization indices in chemical bond-breaking processes lies in the nonlinear mapping between intersite distances and correlation parameters. Although the long-range asymptotic decay of delocalization indices is exponential, we show that as the correlation parameter decreases quantum mechanical interference sets in and a switch to an oscillating pattern, related to core chemical concepts such as resonance or mesomerism, appears.
The one-body picture underlies our understanding of weakly interacting solids but breaks down in strongly correlated systems. We develop a general framework, based on the single-particle Green's function and the one-body reduced density matrix (1RDM), to characterize correlated electronic phases. Applying it to the Hubbard diamond chain, we combine density matrix renormalization group and cellular dynamical mean-field theory to construct symmetry-resolved effective orbitals and track their evolution across its Mott transitions, while the 1RDM purity provides a scalar indicator of the phase boundaries. These tools offer a general route to extend one-body concepts to correlated materials.
We present a new quantum molecular dynamics (MD) method where the electronic structure and atomic forces are solved by a real-space dynamical mean-field theory (DMFT). Contrary to most quantum MD methods that are based on effective single-particle wave functions, the DMFT approach is able to describe correlation-induced Mott metal-insulator transitions and the associated incoherent electronic excitations in an atomic liquid. We apply the DMFT-MD method to study Mott transitions in an atomic liquid model which can be viewed as the liquid-state generalization of the Hubbard model. The half-filled Hubbard liquids also provide a minimum model for alkali fluid metals. Our simulations uncover two distinct types of Mott transition depending on the atomic bonding and short-range structures in the electronically delocalized phase. In the first scenario where atoms tend to form dimers, increasing the Hubbard repulsion gives rise to a transition from a molecular insulator to an atomic insulator with a small window of enhanced metallicity in the vicinity of the localization transition. On the other hand, for Hubbard liquids with atoms forming large conducting clusters, the localization of electrons leads to the fragmentation of clusters and is intimately related to the liquid-gas transition of atoms. Implications of our results for metal-insulator transitions in fluid alkali metals are discussed.
The one-dimensional Hubbard model is investigated by means of two different cluster schemes suited to introduce short-range spatial correlations beyond the single-site dynamical mean-field theory, namely, the cellular dynamical mean-field theory, which does not impose the lattice symmetries, and its periodized version in which translational symmetry is recovered. It is shown that both cluster schemes are able to describe with extreme accuracy the evolution of the density as a function of the chemical potential from the Mott insulator to the metallic state. Using exact diagonalization to solve the cluster-impurity model, we discuss the role of the truncation of the Hilbert space of the bath, and propose an algorithm that gives higher weights to the low-frequency hybridization matrix elements and improves the speed of the convergence of the algorithm.
Correlated electronic systems involve strong shortrange repulsion. At integer filling, the primary effect of correlation is the emergence of an insulating state where band theory predicts a metal. Understanding the transition from a metal to this ‘Mott insulator’, as interaction strength is increased, and the effect of doping the Mott state, are classic problems in quantum many-body physics. They have been explored for decades, starting with the approximate solutions of Hubbard. The real breakthrough came in the 1990s with the advent of dynamical mean field theory, which mapped the correlated system to an embedded single site, and described the detailed spectral evolution across the Mott transition. The only deficiency in this approach is the neglect of spatial correlations, and, possibly, the lack of some ‘visual intuition’ about the transition. We discuss a complementary approach, which provides a reasonable description of Mott physics in a real-space setting and allows a certain degree of visualization. This article provides a pedagogical review of our approach and presents some illustrative results.
One-body reduced density-matrix functional (1RDMF) theory has yielded promising results for small systems such as molecules, but has not addressed quantum phase transitions such as the Mott transition. Here we explicitly execute the constrained search within a variational ansatz to construct a 1RDMF for the multi-orbital Hubbard model with up to seven orbitals in the thermodynamic limit. The variational ansatz is the \mathcal{N}=3 ansatz of the variational discrete action theory (VDAT), which can be exactly evaluated in d=\infty. The resulting 1RDMF exactly encapsulates the \mathcal{N}=3 VDAT results, which accurately captures Mott and Hund physics. We find that non-analytic behavior emerges in our 1RDMF at fixed integer filling, which gives rise to the Mott transition. We explain this behavior by separating the constrained search into multiple stages, illustrating how a nonzero Hund exchange drives the continuous Mott transition to become first-order. Our approach creates a new path forward for constructing an accurate 1RDMF for strongly correlated electron materials.