Correlation and confinement induced itinerant ferromagnetism in chain structures

Abstract

International audienceUsing a positive semidefinite operator technique one deduces exact ground states for a zig-zag hexagon chain described by a non-integrable Hubbard model with on-site repulsion. Flat bands are not present in the bare band structure, and the operators $\hat B^{\dagger}_{\mu,\sigma}$ introducing the electrons into the ground state, are all extended operators and confined in the quasi 1D chain structure of the system. Consequently, increasing the number of carriers, the $\hat B^{\dagger}_{\mu,\sigma}$ operators become connected i.e. touch each other on several lattice sites. Hence the spin projection of the carriers becomes correlated in order to minimize the ground state energy by reducing as much as possible the double occupancy leading to a ferromagnetic ground state. This result demonstrates in exact terms in a many-body frame that the conjecture made at two-particle level by G. Brocks et al. [Phys.Rev.Lett. {\bf 93},146405, (2004)] that the Coulomb interaction is expected to stabilize correlated magnetic ground states in acenes is clearly viable, and opens new directions in the search for routes in obtaining organic ferromagnetism. Due to the itinerant nature of the obtained ferromagnetic ground state, the systems under discussion may have also direct applicatio

Itinerant surfaces with spin-orbit couplings, correlations and external magnetic fields: exact results

“…For this reason we use the method based on positive semidefinite operator properties whose applicability does not depend on dimensionality and integrability [13][14][15][16] . The method has been previously applied in conditions unimaginable before in the context of exact solutions in 1-3D, even in the presence of the disorder [17][18][19][20][21][22][23][24] .…”

Ferromagnetism without flat bands in thin armchair nanoribbons

“…As Figs. (11,12) show, flat bands in the bare band structure are not present for non-zero values of allĤ 0 parameters. This fact can be directly and analytically verified in the following way.…”

Exact ground states for polyphenylene type of hexagon chains

“…To deduce exact ground states in such a case one uses a technique based on positive semidefinite operator properties whose applicability does not depend on dimensionality or integrability. The procedure itself has been described previously in details in several publications [16,17], provides results even in circumstances unexpected in the context of exact solutions as systems in two [18], or three [16] dimensions, disordered systems [19] or textures [20], being also intensively tested for chain structures [17,21,22] including hexagonal type of chains as well [23,24]. Using the method, one transforms the HamiltonianĤ in positive semidefinite form (i.e.Ĥ = nP n + E g , whereP n are positive semidefinite operators, while E g is a scalar) and looks for the most general wave vector |Ψ g with the property nP n |Ψ g = 0.…”