Wagner research group

Incomplete concept inventory

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
  • LaTiO3
  • 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