Gunnarsson-Sheath model
The Gunnarsson-Sheath (GS) model is a phenomenological quantum many-body theory (QM) used to describe the emergence of collective properties in quantum dynamic systems. The model was developed by the Swedish physicist Ove Gunnarsson and his colleague Jürgen Sheath to describe spin-dependent correlations in atoms and molecules. While the original formulation of the GS model was developed to describe spin-correlations, it has since been extended to address other aspects of strongly-interacting systems such as bonding, structural transitions, and polarization of molecules.
In the GS model, the full many-body wave function of a system is expressed as a linear combination of single-reference formulae that embodying the necessary correlations. This is known as a single Slater-determinant approximation (SDA). The GS model avoids the use of specialized distributions and instead uses only the eigenvalues and eigenvectors of the underlying Hamiltonian of the system. This allows the model to capture general features of strongly-interacting systems.
The GS Hamiltonian is composed of two terms: an one-body part, depending only on the spin components of the system, and an antiferromagnetic coupling term describing interactions between different spin states. This is expressed as:
H = -J S^2 + g [S(r_1) S(r_2)+...+S(r_N)]
where J and g are constants, and S(r_i) are the spin components at various positions r_i. The first term (the Heisenberg model) is the Ising term, containing the exchange coupling between spins, while the second term is an antiferromagnetic coupling term describing the interaction between spins at different positions.
The GS model is designed to be used in the context of correlated electrons, where electrons interact with each other during transitions. In this case, the Hamiltonian contains an additional term representing the electron correlation energy, given by E_corr = g_0 S(r_1) S(r_2), where g_0 is the correlation coupling. This term depend on the relative positions of the electrons, and is included to better describe condensed matter such as solids and liquids.
The GS model is a powerful tool for describing various phenomena in strongly-interacting systems. In particular, it has been successfully applied to describe spin correlations in atoms and molecules, and to model the electronic structure of condensed matter. In addition, it can be used to study transitions between insulators and metals, phase transitions in matter, and even to describe the atomic structure of solids.
Examples of applications of the GS model can be found in the fields of chemistry and condensed matter physics. In chemistry, the GS model has been used to study the electronic structure of molecules and to predict the electronic properties of certain compounds. For example, the GS model has been successfully used to study the energetics of ions and electrons in atoms, to predict the spin-orbit excitation energies of molecules, and to predict the dissociation energies of molecules.
In condensed matter physics, the GS model has been successfully used to study the electronic structure of solids, such as band structures of semiconductors, the quantum Hall effect, and the charge-density-wave (CDW) transition in heavy-fermion materials. In addition, the GS model has been used to study the dynamics of Josephson junctions, to explain the Mott insulating phase in certain materials, and to study the physics of superconductivity.
In conclusion, the GS model is an important tool for understanding and predicting physical phenomena in strongly-interacting quantum systems. It has been used to study the electronic structure of molecules, to describe the electronic structures of solids, and to study phase transitions in materials. Moreover, owing to its flexibility and simplicity, the GS model has found applications in many different fields, such as chemistry, condensed matter physics, and quantum information.
