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Interactions beyond independent particles

Investigate correlated electronic systems through solvable limits, controlled approximations, spectral diagnostics, and explicitly identified unresolved phase questions.

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10 published lessons1 module350 min of guided study

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  1. 01
    Interactions beyond independent particlesresearch · 10 lessons

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Module 01 research

Interactions beyond independent particles

Investigate correlated electronic systems through solvable limits, controlled approximations, spectral diagnostics, and explicitly identified unresolved phase questions.

  1. 01

    Hubbard atomic limit and the Mott gap

    Solve the repulsive one-orbital atomic limit while separating a charge gap from magnetic ordering and lattice transition claims.

    35 min
  2. 02

    Superexchange from a strong-coupling expansion

    Derive antiferromagnetic exchange from virtual double occupancy and benchmark its coefficient against an exact dimer.

    35 min
  3. 03

    Green-function spectral weight and sum rules

    Connect addition and removal spectra to canonical anticommutators and use normalization as a stringent numerical diagnostic.

    35 min
  4. 04

    Fermi-liquid quasiparticle residue

    Derive a narrow pole from the self-energy and distinguish its residue, lifetime, velocity and Fermi-volume constraint.

    35 min
  5. 05

    One-dimensional bosonization and Luttinger liquids

    Replace low-energy fermion density fluctuations by collective fields while keeping spin, charge and commensuration assumptions explicit.

    35 min
  6. 06

    Dynamical mean-field self-consistency

    Map a lattice model to a dynamical impurity bath and state precisely which limit makes a local self-energy exact.

    35 min
  7. 07

    Anderson localization and disorder

    Distinguish interference-induced localization from an interaction gap and test spatial participation without overinterpreting a finite sample.

    35 min
  8. 08

    Quantum-critical metal scaling

    Test scaling hypotheses near a zero-temperature transition without treating a collapse or linear resistivity as a unique microscopic diagnosis.

    35 min
  9. 09

    Heavy fermions and Kondo lattices

    Separate single-moment screening from lattice coherence, and track spin conventions and Fermi-volume assumptions.

    35 min
  10. 10

    Pseudogap observations and competing interpretations

    Separate a partial depletion of electronic spectral weight from the hypotheses used to explain it, with explicit probe and temperature qualifications.

    35 min
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