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MultiScience - XXXIII. microCAD International Multidisciplinary Scientific Conference

Many-body spin-orbit coupling in two dimensional correlated itinerant systems in the presence of external in-plane magnetic

Nóra Kucska, Zsolt Gulácsi

Published Jan 1, 2019• 0 citations

Abstract

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.

DOI: 10.26649/musci.2019.023

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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.

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.

Using a positive semidefinite operator technique we deduce 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 , introducing the electrons into the ground state, are all extended operators and confined in the quasi-1D chain structure of the system. Consequently, by increasing the number of carriers, the 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 the two-particle level by G. Brocks et al., [Phys. Rev. 93 (2004) p.146405.] that the Coulomb interaction is expected to stabilize correlated magnetic ground states in acenes, is clearly viable, and opens up 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 also have direct application possibilities in spintronics.

The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.

We study itinerant ferromagnetism in multi-orbital 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 any generic filling factor 0 < n < 2 (0 < n < 3) in two (three) dimensions. Possible applications to p-orbital bands with ultra-cold fermions in optical lattices are discussed.

Correlation effects in the one-dimensional Hubbard model are studied by application of the L-resolvent method. The calculations are well beyond one-particle mean field approximation. All correlations involving two neighboring sites are included exactly and higher order correlations are approximated. The effects of varying temperature, band filling, Coulomb repulsion and external magnetic field are investigated. Two-site correlations for non-half-filled band fillings are calculated for the first time. Some exact relations between correlation functions are derived by electron-hole symmetry. Results indicate that short-range spin correlations always favor antiferromagnetic order. Large Coulomb repulsion induces a gap in the excitation spectrum and a metal-insulator transition is predicted as the Coulomb repulsion parameter is changed.