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Register a new userThe adiabatic strictly-correlated-electrons functional: kernel and exact properties
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We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Within the latter, we derive an analytical expression for the adiabatic SCE Hartree exchange-correlation kernel in one dimensional systems, and we compute it numerically for a variety of model densities. We analyse the non-local features of this kernel, particularly the ones that are relevant in tackling problems where kernels derived from local or semi-local functionals are known to fail.
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Modern density functional theory (DFT) calculations employ the Kohn-Sham (KS) system of non-interacting electrons as a reference, with all complications buried in the exchange-correlation energy (Exc). The adiabatic connection formula gives an exact expression for Exc. We consider DFT calculations that instead employ a reference of strictly-correlated electrons. We define a decorrelation energy that relates this reference to the real system, and derive the corresponding adiabatic connection formula. We illustrate this theory in three situations, namely the uniform electron gas, Hookes atom, and the stretched hydrogen molecule. The adiabatic connection for strictly-correlated electrons provides an alternative perspective for understanding density functional theory and constructing approximate functionals.
The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this limit is expected to yield strictly-correlated particle positions, related to each other by co-motion functions (or optimal maps), but the existence of such a deterministic solution in the general three-dimensional case is still an open question. A conjecture for the co-motion functions for radially symmetric densities was presented in Phys.~Rev.~A {bf 75}, 042511 (2007), and later used to build approximate exchange-correlation functionals for electrons confined in low-density quantum dots. Colombo and Stra [Math.~Models Methods Appl.~Sci., {bf 26} 1025 (2016)] have recently shown that these conjectured maps are not always optimal. Here we revisit the whole issue both from the formal and numerical point of view, finding that even if the conjectured maps are not always optimal, they still yield an interaction energy (cost) that is numerically very close to the true minimum. We also prove that the functional built from the conjectured maps has the expected functional derivative also when they are not optimal.
We construct a class of exact ground states for correlated electrons on pentagon chains in the high density region and discuss their physical properties. In this procedure the Hamiltonian is first cast in a positive semidefinite form using composite operators as a linear combination of creation operators acting on the sites of finite blocks. In the same step, the interaction is also transformed to obtain terms which require for their minimum eigenvalue zero at least one electron on each site. The transformed Hamiltonian matches the original Hamiltonian through a nonlinear system of equations whose solutions place the deduced ground states in restricted regions of the parameter space. In the second step, nonlocal product wave functions in position space are constructed. They are proven to be unique ground states which describe non-saturated ferromagnetic and correlated half metallic states. These solutions emerge when the strength of the Hubbard interaction $U_i$ is site dependent inside the unit cell. In the deduced phases, the interactions tune the bare dispersive band structure such to develop an effective upper flat band. We show that this band flattening effect emerges for a broader class of chains and is not restricted to pentagon chains. For the characterization of the deduced solutions, uniqueness proofs, exact ground state expectation values for long-range hopping amplitudes and correlation functions are also calculated. The study of physical reasons which lead to the appearance of ferromagnetism has revealed a new mechanism for the emergence of an ordered phase, described here in details (because of lack of space see the continuation in the paper).
We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the f-orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons, U_d, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher dimensional models. We find that this interaction shifts and widens the energy range of the bare f-level, where heavy-fermion behavior can be observed. For large enough U_d this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while U_d enhances the quasi-particle mass when the filling is close to half filling.
Strongly correlated electrons on an Apollonian network are studied using the Hubbard model. Ground-state and thermodynamic properties, including specific heat, magnetic susceptibility, spin-spin correlation function, double occupancy and one-electron transfer, are evaluated applying direct diagonalization and quantum Monte Carlo. The results support several types of magnetic behavior. In the strong-coupling limit, the quantum anisotropic spin 1/2 Heisenberg model is used and the phase diagram is discussed using the renormalization group method. For ferromagnetic coupling, we always observe the existence of long-range order. For antiferromagnetic coupling, we find a paramagnetic phase for all finite temperatures.
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