Physics / research
Quantum matter and many-body methods
Study emergent quasiparticles, bands, interacting fermions, condensates, topological phases, and entanglement diagnostics.
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Module 01 research
Quantum matter and many-body methods
Study emergent quasiparticles, bands, interacting fermions, condensates, topological phases, and entanglement diagnostics.
- 01
Second quantization and lattice Hamiltonians
Build many-particle lattice models from occupation states, fermionic operators, hopping, and local interactions.
40 min - 02
Bloch bands and reciprocal space
Derive crystal momentum, Brillouin-zone equivalence, and the tight-binding band of a periodic chain.
40 min - 03
Phonons and collective modes
Find normal modes of a harmonic chain and explain why quantizing their collective motion produces phonons.
40 min - 04
Fermi surfaces and Fermi liquids
Count a filled Fermi sea and explain how long-lived interacting quasiparticles organize low-energy metallic behavior.
44 min - 05
Hartree–Fock and variational states
Optimize an antisymmetric product state, separate direct and exchange energies, and diagnose the limits of self-consistent mean field.
44 min - 06
The Hubbard model and Mott localization
Separate interaction-driven charge localization from a filled-band insulator and derive superexchange in a controlled limit.
29 min - 07
Bose condensation and Bogoliubov theory
Derive the excitation scale of a dilute repulsive Bose gas and separate condensation, coherence, and superfluid response.
28 min - 08
BCS pairing and superconductivity
Build a paired fermionic variational state, calculate its gapped excitations, and identify the limits of weak-coupling mean field.
30 min - 09
Berry phase and topological bands
Distinguish gauge-dependent band eigenvectors from geometric phases and calculate a symmetry-protected one-dimensional winding.
30 min - 10
Entanglement and tensor-network states
Use Schmidt weights to quantify bipartite entanglement and understand when matrix-product states compress quantum matter.
31 min