Pairing enhancement in Betts lattices with next nearest neighbor couplings: Exact results

TL;DR

This paper investigates electron pairing phenomena in Betts lattices with next nearest neighbor couplings using exact diagonalization, revealing conditions for phase transitions and pairing enhancement in finite two-dimensional systems.

Contribution

It provides exact results on pairing and phase transitions in Betts lattices with next nearest neighbor couplings, extending previous bipartite geometry studies.

Findings

Identification of spin and charge coherent pairing regions.

Demonstration of temperature-driven crossover contours.

Criteria for smooth and abrupt phase transitions.

Abstract

Electron instabilities in the Hubbard model with the next nearest neighbor coupling are calculated by exact diagonalization in finite, two-dimensional Betts cells (lattices). A viable spin and charge coherent pairing, signaled by quantum critical points and a negative charge gap region, is found in 8- and 10-site Betts lattices at small and moderate U regions consistent with our exact results in elementary bipartite geometries [Phys. Rev. B 78 (2008) 075431]. The contour isolines for continuous temperature driven-crossover between the Mott-Hubbard insulating and coherent pairing phases are demonstrated. The criteria for smooth and abrupt phase transitions are found for systematic enhancement of coherent pairing by optimization of the next nearest neighbor coupling parameter.