Open notebook · Theory into practice

A working library for many-body calculations.

These notes connect physical intuition, mathematical derivations, and implementation details. They are written to be revisited—not merely read once.

Browse by subject

Choose an entry point

Each collection begins with the essential picture, then moves toward equations and computational choices.

Dyson’s equation, GF2, GW, screened interactions, and self-consistent vertex corrections.

Build intuition for charge transport, crystals, and electronic behavior in solids.

Tensor hypercontraction and cross interpolation for high-dimensional many-body problems.

Coulomb integrals, quasiparticles, notation, and reusable physical concepts.

Suggested sequence

Start with a classical model, add the language of excitations, then move into interacting and compressed representations.

01
Physical intuition
The Drude model
From collisions to DC and optical conductivity.
02
Many-body language
Quasiparticles
Poles, lifetimes, spectral weight, and the self-energy.
03
Interaction
Two-electron integrals
The four-index object behind electronic correlation.
04
Approximation
GW and GF2
Two conserving views of the electronic self-energy.
05
Beyond GW
Vertex corrections
Where Γ enters and what screened exchange changes.
06
Factorization
Tensor hypercontraction
Compress the Coulomb tensor without hiding the approximation.
07
Adaptive sampling
TT cross interpolation
Query only the tensor entries that carry the structure.

How to read these notes

Definitions establish a shared notation before calculations begin.

Equations are followed by interpretation, limits, and computational meaning.

Primary references make every page a launch point for deeper study.