Abstract
In the framework of numerical calculations and analytical expansion in the transfer integral between the next-nearest neighbors t’ and the direct antiferromagnetic (AFM) gap ∆, the metal–insulator transition criterion is obtained, the Hartree-Fock and slave boson approaches being used. In the case of a square lattice, there is an interval of t’ values, for which the metal-insulator transition is a first-order transition, which is due to the Van Hove singularity near the center of the band. For simple and body-centered cubic lattices, the transition from the insulator AFM state occurs to the phase of an AFM metal and is a second-order phase transition; it is followed by a transition to a paramagnetic metal. These results are modified when taking into account the intersite Heisenberg interaction which can induce first-order transitions.
Highlights
The nature of the metal—insulator transition in strongly correlated systems is still not understood in detail
In the case of a square lattice, there is an interval of t values, for which the metalinsulator transition is a first-order transition, which is due to the Van Hove singularity near the center of the band
For simple and body-centered cubic lattices, the transition from the insulator AFM state occurs to the phase of an AFM metal and is a second-order phase transition; it is followed by a transition to a paramagnetic metal
Summary
The nature of the metal—insulator transition in strongly correlated systems is still not understood in detail. The competition between the insulator antiferromagnetic (AFM) state and the paramagnetic one gives the phase boundary of the metal—insulator transition of the first order [1]. Since at half-filling the correlation narrowing of the spectrum occurs uniformly by the factor zA2 FM, we have for the gap at the boundary of the transition into AFM metal. It follows from Eq (34) that the correlation correction, proportional to ζ0, leads to a larger increase in the energy of the AFM insulator phase than of the PM phase This means that the correlation contributions expand the firstorder transition region, or even can turn the second-order transition into a first-order transition. Taking into account the direct exchange interaction in the framework of the Hartree-Fock approximation will lead to the replacement of U by Ueff (Q) only, which cannot change the type of transition. The role of the exchange correction depends on the sign of J: antiferromagnetic exchange stabilizes the AFM state expanding the region of the second order transition, and the ferromagnetic exchange destabilizes it and leads to first-order transition
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