Condensed-Matter Models
Condensed-matter model cards summarize standard lattice and band models used to teach hopping, band formation, Dirac points, topology, and superconducting mean-field phases. They are lookup cards: Quantum Matter Reference and Data routes a requested model to its material-facing convention and provenance record and to the page that owns its physics; these cards retain compact model identification and assumptions.
| Model | Main lesson | Core formalism |
|---|---|---|
| Tight-Binding Chain | Nearest-neighbor hopping produces a cosine band | Bloch Theorem |
| Graphene Dirac Model | Honeycomb sublattices give valley Dirac cones | Bloch Theorem |
| SSH Model | Dimerized hopping realizes a one-dimensional winding invariant | Berry Curvature |
| Kitaev Chain | A one-dimensional p-wave superconductor supports Majorana end modes in its topological phase | Topological Invariants |
Shared Checklist
Section titled “Shared Checklist”For any condensed-matter model, specify:
- lattice geometry and boundary conditions;
- orbitals or sublattices per unit cell;
- whether spin, interactions, disorder, and magnetic fields are included;
- hopping, onsite, pairing, or mass-term conventions;
- Brillouin-zone convention and lattice spacing;
- symmetry assumptions used for any topological statement.
Common Mistakes
Section titled “Common Mistakes”- Treating a band Hamiltonian as a complete material model.
- Forgetting spin, valley, sublattice, orbital, or boundary-condition degeneracies.
- Comparing topological phases without checking which symmetries are preserved.
- Applying a low-energy Dirac expansion far from the expansion point.
- Treating edge states as automatic without specifying termination and gap assumptions.
References
Section titled “References”- N. W. Ashcroft and N. D. Mermin, Solid State Physics, Holt, Rinehart and Winston, 1976.
- S. H. Simon, The Oxford Solid State Basics, Oxford University Press, 2013.
- B. A. Bernevig and T. L. Hughes, Topological Insulators and Topological Superconductors, Princeton University Press, 2013.
- J. K. Asbóth, L. Oroszlány, and A. Pályi, A Short Course on Topological Insulators, Springer, 2016.