A 2D square, two-bands, strongly correlated and non-integrable system is analysed exactly in the presence of many-body spin-orbit interactions via the method of Positive Semidefinite Operators.The deduced exact ground states in the high concentration limit are strongly entangled, and given by the spin-orbit coupling are ferromagnetic and present an enhanced carrier mobility, which substantially differs for different spin projections. The described state emerges in a restricted parameter space region, which however is clearly accessible experimentally. The exact solutions are provided via the solution of a matching system of equations containing 74 coupled, non-linear and complex algebraic equations. In our knowledge, other exact results for 2D interacting systems with spin-orbit interactions are not present in the literature.

We analyze, in exact terms, multiband 2D itinerant correlated fermionic systems with manybody spin-orbit interactions, and in-plane external magnetic fields. Even if such systems with broad applicability in leading technologies are non-integrable, we set up an exact solution procedure for them, which is described in details. Casting the Hamiltonian in positive semidefinite form, the technique leads to the ground state, and also characterizes the low lying excitation spectrum.PACS numbers:

The ferromagnetism of Au nanograins is analyzed based on a two-dimensional itinerant lattice model with on-site Coulomb repulsion, many-body spin–orbit interactions, and holding two hybridized bands, one correlated and one uncorrelated. Using periodic boundary conditions in both directions, an exact ferromagnetic ground state is deduced for this non-integrable system by applying special techniques based on positive semidefinite operators.

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