Lattice models in condensed matter

Lattice models represent particles or degrees of freedom on discrete sites arranged in a lattice. They simplify condensed-matter systems while retaining interactions and collective behavior shaped by the lattice.

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Bravais lattice: An infinite array of points generated by translations of a primitive unit cell. It supplies the periodic geometry on which many lattice models are defined.
Hopping (physics): The transfer of a particle between localized states on different sites. Hopping sets the kinetic energy scale in many lattice Hamiltonians.
Kagome lattice: A two-dimensional lattice of corner-sharing triangles with a geometry that frustrates many spin configurations. Its geometry creates unusual magnetic states in lattice spin models.
Continuum model: A model that describes physical quantities as fields varying continuously across space. It replaces discrete sites with spatially continuous degrees of freedom.
Felix Bloch: A Swiss-American physicist who developed the theory of electron waves in periodic crystals. Bloch's work established how periodic lattices shape electronic states.
Tight-binding model: A quantum model in which particles occupy localized states and move between sites through hopping. It turns lattice sites and intersite motion into a simple electronic description.
On-site interaction: An interaction energy associated with multiple particles occupying the same lattice site. It competes with hopping and can suppress charge motion.
Quantum spin liquid: A magnetic state with strong quantum fluctuations and no conventional long-range magnetic order. Spin lattices provide candidate settings for this elusive phase.
Free-electron model: An approximation that treats conduction electrons as independent particles moving through a solid. It neglects much of the site-specific interaction structure retained by lattice models.
Bloch's theorem: A result stating that eigenstates in a periodic potential are plane waves multiplied by periodic functions. It provides the foundation for describing electrons in crystalline lattices.