This is a concept inventory for things that we work on in our group

Phenomena

Superconductivity
Magnetism
- Ferro
- Anti-ferro
- Spin glass
- Spin ice
Quantum spin hall effect
Rashba effect
Ferroelectricity/polarization in materials
Phonons
Electron-phonon coupling
Spin-orbit coupling

Fundamental simplified systems/Hamiltonians

Hubbard model
Homogeneous electron gas
Unitary gas (contact interaction)
Hydrogen chain
Heisenberg model
Ising model
Kane-Mele model
Kitaev model
RVB state

Characteristic or benchmark real systems

Silicon
Diamond
Graphene
VO₂
Cuprates
Perovskites
Spinels
Transition metal dichalchogenides

Concepts in chemistry

Orbital hybridization
Bonding/antibonding orbitals

Numerical quantum Methods

Coupled cluster
Density Matrix Renormalization Group (DMRG)
Configuration Interaction
Perturbation theory (MP2)
Green function (GW and GF2)
Density Matrix Downfolding
Quantum Monte Carlo
Time dependent DFT
Density functional theory
Numerical renormalization group

Computer tools

Using shell (bash)
Python - packages
- pandas
- seaborn
- matplotlib
- snakemake
- pyscf
- pyqmc
- virtual environments
- packaging
Conda
Coding standards and styles
Debugging techniques
Other tools
- rsync
- ssh
- ssh tunneling

Concepts in mathematics

Core math

Central limit theorem
Monte Carlo integration
Statistical inference
Bootstrap method

Mathematical objects useful in many-body quantum

Berry phase
Many-particle wave function
Effective field theory
Effective Hamiltonian
Effective Lagrangian
Topological invariant
Mermin-Wagner theorem
Reduced density matrices

Approximations

Born-Oppenheimer approximation