Abstract
In contrast to the Hubbard model, the extended Hubbard model, which additionally accounts for non-local interactions, lacks systemic studies of thermodynamic properties especially across the metal-insulator transition. Using a variational principle, we perform such a systematic study and describe how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator. The thermodynamics reveal that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials.
Highlights
B Error estimation B.1 Statistical determinant quantum Monte Carlo (DQMC) Errors B.2 Systematic DQMC errors B.3 Errors related to the free energy B.4 Finite-size convergence for the Coulomb case
We briefly review the nature of this maximum to set the stage for the discussion of effects from non-local interactions
Disregarding long-range anti-ferromagnetic fluctuations the double occupancy first decreases with temperature, since the formation of unordered local moments gains entropy over itinerant electrons
Summary
The Hubbard model [1,2,3,4,5] of itinerant electrons with a local interaction is arguably the simplest model describing the competition between kinetic energy and interaction. It is of enormous importance for the understanding of strongly correlated materials and it is not surprising that much effort has been spent on unveiling its properties through analytical, numerical, and experimental methods. Systematic studies of thermodynamic properties are rare and reference data for detailed comparisons and benchmarks between methods especially in context of the metal-insulator transition is missing. We start by introducing the model and method of approximation in the following Secs. 2.1 and 2.2
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