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 set up and describe in details an exact solution procedure for a 2D itinerant correlated fermionic many-body system in the presence of spin-orbit interactions, onsite Coulomb repulsion in the correlated band, and in-plane external magnetic fields.The model is non-integrable, but using the method based on positive semidefinite operator properties, exact ground states are provided below half filling, at 3/4, and above 3/4 filling.The presented technique provides the possibility to study in exact terms a 2D phenomenon with broad applicability in leading technologies. I.
Based on a positive semidefinite operator technique, exact ground states are deduced for the non-integrable conducting polymers possessing pentagon type of unit cell. The study is done in the presence of many-body spin-orbit interaction (SOI), local and nearest neighbor Coulomb repulsion (NNCR) and presence of external
E electric and
B magnetic fields, such that the effects of
B on both orbital and spin degrees of freedom is considered. The SOI, NNCR, and presented external field configurations presence in exact conducting polymer ground states is a novelty, so the development of the technique for the treatment possibility of such strongly correlated cases is presented in details. The deduced ground states show a broad spectrum of physical characteristics ranging from charge density waves, metal-insulator transitions, to interesting external field driven effects as e.g. modification possibility of a static charge distribution by a static external magnetic field.
We investigate the correlation effects on spin-orbit coupling (SOC) in a two-orbital Hubbard model on a square lattice by applying the variational Monte Carlo method. We consider an effective SOC constant
λeff in the one-body part of the variational wave function and mainly discuss the cases of the electron number per site
n=1, that is, quarter filling. We find that
λeff is proportional to the bare value
λ and depends on the electron-electron interactions through
(U′−J′) in a relatively wide parameter range in the paramagnetic (PM) phase, where
U′ is the interorbital Coulomb interaction and
J′ is the pair hopping interaction. Increasing the electron-electron interactions in the PM phase leads to a transition to an effective one-band state, in which the upper band becomes empty due to the enhanced
λeff. We also construct phase diagrams considering magnetic order. The carrier doping effect on
λeff is also investigated. We find that
λeff enhances in a strongly correlated region around the Mott transition point and it is necessary to include the correlation effects beyond the Hartree-Fock approximation to describe the enhanced SOC properly.
We study the ground state properties of spin-half bosons subjected to the Rashba spin-orbit coupling in two dimensions. Due to the enhancement of the low energy density of states, it is expected that the effect of interaction becomes more important. After reviewing several possible ideal condensed states, we carry out an exact diagonalization calculation for a cluster of the bosons in the presence of strong spin-orbit coupling on a two-dimensional disk and reveal strong correlations in its ground state. We derive a low-energy effective Hamiltonian to understand how states with strong correlations become energetically more favorable than the ideal condensed states.
We study itinerant ferromagnetism in multiorbital Hubbard models in certain two-dimensional square and three-dimensional cubic lattices. In the strong coupling limit where doubly occupied orbitals are not allowed, we prove that the fully spin-polarized states are the unique ground states, apart from the trivial spin degeneracies, for a large region of filling factors. Possible applications to
p-orbital bands with ultracold fermions in optical lattices, and electronic
3d-orbital bands in transition-metal oxides, are discussed.