Lecture Notes
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Correlated Electrons and Quantum Magnetism
Hubbard model, Hartree–Fock theory for general magnetic order, spin waves in the ladder-sum approximation and the spin stiffness, Coulomb matrix elements, and the strong-coupling expansion to the Heisenberg model, J = 4t2/U.
Hubbard modelspin wavesquantum magnetism -
Quantum Spin Liquids and the Projective Symmetry Group
Parton mean-field theory, gauge fluctuations, Gutzwiller projection, Schwinger bosons, and the projective symmetry group, with the Z2 PSGs of Schwinger bosons on the triangular lattice worked out in full.
spin liquidspartonsPSG -
Landau levels, the Bloch bundle, Berry phase and Chern numbers, two-band Dirac models, bulk–edge correspondence, spontaneous symmetry breaking, the kink, and the abelian and non-abelian Higgs mechanism.
topological insulatorsChern numberHiggs mechanism -
Replica Fluctuations and the Replicon
Stability of the replica-symmetric solution of the Sherrington–Kirkpatrick model: longitudinal, anomalous and replicon sectors, the de Almeida–Thouless line, Parisi replica-symmetry breaking, ultrametricity, and the Nishimori line. With exercises and solutions.
spin glassesreplica theoryNishimori line -
Renormalization in a one-dimensional scattering problem, Kadanoff block spins and scaling, Wilson's fixed points and scaling fields, exact decimation of the Ising chain, and the idea of the ε expansion.
renormalization groupcritical phenomenaIsing model
Calculation Notes
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When Is a Measurement RG-Relevant?
A step-by-step guide to the R to 1 replica trick, the measurement Harris criterion, and the 2D Ising spin and energy examples.
replica theorymeasurementrenormalization groupIsing CFT -
Rokhsar-Kivelson States, Noisy Ising Measurements, and Mixedness
A detailed Ising note deriving the RK wavefunction, the Bayesian posterior under noisy bond measurements, the exact outcome-averaged mixed state, and the first-moment identity.
RK statesIsing modelmeasurementsmixed statesNishimori line -
From quenched disorder to Bayesian conditioning, with replica limits, Nishimori-line symmetries, and gauge interpretations.
replica theorystatistical mechanicsBayesian inference