Tight binding is a fundamental model in condensed matter physics and solid state physics that is used to describe the electronic structure of solids. The tight binding model focuses on the behavior of electrons in a crystal lattice, particularly how their wave functions are influenced by the periodic potential created by the lattice. ### Key Concepts: 1. **Lattice Structure**: In the tight binding model, the material is represented as a lattice of atoms, each of which has a discrete number of occupied electronic states.
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Tight binding approximates a quantum system using orbitals localized near sites and Hamiltonian matrix elements describing their energies and hopping. In a one-dimensional chain with one orbital per cell and nearest-neighbor hopping,A Bloch state gives the dispersion and bandwidth .
The finite bandwidth makes explicit how overlap between localized states produces delocalized bands. More orbitals, longer-range hopping, spin and magnetic phases give richer matrices. A localized-orbital basis is an approximation to the physical problem, and its parameters must be obtained from a microscopic calculation or fit. The hopping amplitude is a matrix element, not a probability of a completed stochastic hop.