Exact ground states for polyphenylene type of hexagon chains

Abstract

This article is dedicated to Dieter Vollhardt on the occasion of his 60th birthday.A technique based on positive semidefinite operator properties has been used in deducing exact ground states for hexagon chains of polyphenylene type (hexagons interconnected by bonds build up the 1D periodic structure), placed in a constant external magnetic field B perpendicular to the surface containing the system. The used Hubbard type of model takes into account B by Peierls phase factors, and has the peculiar property to provide only flat bands in the bare band structure for elevated external field values independent on the parameters entering in the kinetic part of the Hamiltonian. The deduced ground states are non-magnetic or ferromagnetic in character, localized in the thermodynamic limit, and besides the fact that B is able to switch the system between different phases, emphasize that the localization length and connectivity conditions can be tuned by external magnetic fields.

Interaction-created effective flat bands in conducting polymers

“…However, in recent years, it becomes clear that in conducting and periodic organic systems, the Coulomb interaction between the carriers plays an important role. For example, the on-site Coulomb repulsion may even reach 10 eV 25 , and it was also conjectured that in the highly doped region, the Coulomb interaction would be able to stabilize magnetic order 26 , all this information being considered during theoretical studies 15,16,[27][28][29][30][31][32][33][34] .…”

Magnetic nano-grains from a non-magnetic material: a possible explanation

“…The solution procedure (see [3][4][5][6][7] for details) is based on positive semidefinite operator properties. The technique first transforms in exact terms the Hamiltonian Ĥ of the system in a positive semidefinite form ˆĤ P C = + where P is a positive semidefinite operator while C is a constant scalar.…”

“…The Coulomb repulsion in this many-body system is screened by the itinerant system, consequently is of short-range type, and hence is taken into account for simplicity by the on-site Coulomb repulsion alone. Below this Hubbard system is solved exactly for the ground state in a restricted region of the parameter space, obtaining a ferromagnetic solution for small L values.The solution procedure (see [3][4][5][6][7] for details) is based on positive semidefinite operator properties. The technique first transforms in exact terms the Hamiltonian Ĥ of the system in a positive semidefinite form ˆĤ P C = + where P is a positive semidefinite operator while C is…”