Exact results relating spin–orbit interactions in two-dimensional strongly correlated systems

ABSTRACT

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.

KEYWORDS:

• Strongly correlated electrons
• magnetic order
• low-dimensional structures
• spin-orbit interactions
• exact results

Notes

No potential conflict of interest was reported by the authors.

1 One notes that since for ${\lambda }_f=0$ the ground state (8(8) $$\begin{array}{c}\hfill |{\mathrm{\Psi }}_g⟩=\prod _{\mathbf{i}}\left[\left(\prod _{G=A,B}{\widehat{G}}_{\mathbf{i}}^{†}\right){\widehat{D}}_{\mathbf{i}}^{†}\right]|0⟩,{\widehat{D}}_{\mathbf{i}}^{†}=\left({\gamma }_{\uparrow }{\widehat{f}}_{\mathbf{i},\uparrow }^{†}+{\gamma }_{\downarrow }{\widehat{f}}_{\mathbf{i},\downarrow }^{†}\right),\end{array}$$(8) ) is no more valid, the plot in Figure 4 cannot be started from the origin. But the relation $li{m}_{{\lambda }_f\to 0}{\overline{S}}_n^z=0$ is satisfied.

Additional information

Funding

This work was supported for N.K. by New National Excellence Program of the Hungarian Ministry of Human Capacities [UNKP-17-2], for Z.G. by Hungarian funds for basic research [NKFI-K-128018] and Alexander von Humboldt Foundation [3.3-UNG/1009515-STP].