Link between Ground-State Correlations and Independent-Fermion Entropy

Strongly correlated electrons are investigated in the framework of many-body model Hamiltonians. A novel lattice density functional theory (LDFT) has been developed which successfully applies the fundamental concepts of the density functional theory (DFT) of the inhomogeneous electron gas to discrete lattice models, thereby qualitatively extending the actual scope of DFT. In this way a new perspective to understanding the physics of strongly correlated systems has been achieved. In order to study the properties of narrow-band metals, we considered the periodic Hubbard model. Taking advantage of lattice-translational symmetry, one can express the interaction energy W as a functional of the occupation numbers η_kσ of the one-particle Bloch states. A remarkable correlation between the interaction energy W and the entropy S of the occupation number distribution η_kσ has been discovered, from which a simple but highly effective approximation to the interaction energy functional W[η] has been derived. With the help of this approximation we have successfully calculated the main ground-state properties of the Hubbard model in D = 1 – 3 dimensions, as well as in the limiting case D → ∞. These include the ground-state energy E₀, the average number of double occupations D, the kinetic energy T, the occupation numbers in the ground state η_kσ, and the ground-state single-particle density matrix γ_ijσ (see Figure below). Comparison with the corresponding exact results shows that LDFT yields remarkably accurate results in the whole range from weak to strong correlations including the strongly correlated Heisenberg limit U/t → ∞.

Figure: Ground state properties of the half-filled 1D Hubbard model as a function of the interaction strength U/t. The comparison between LDFT results and exact results for the ground-state energy E₀, number of double occupations D, occupation numbers η_kσ, and single-particle density matrix γ_ijσ demonstrates the accuracy of the method in the whole range from weak to strong correlations.

Reference: T. S. Müller, W. Töws, and G. M. Pastor, Phys. Rev. B 98, 045135 (2018)