This project simulates three different properties of spin-1/2 fermions on a 1D lattice. The file fermi_hubbard_report.pdf contains a full writeup.

ed.py performs exact diagonalization to calculate the energy bands for very small systems (N <= 7) with periodic boundary conditions. Plots the band structure diagram with the Fermi level and highlights the conduction band if any.

mft_phase.py uses mean field theory to calculate the magnetic phase diagram over different densities and interaction strengths.

mft_compressibility.py uses self-consistent mean field theory and Monte-Carlo sampling to compute the dependence of density on external chemical potential, and plots it with the phase associated with each density. Also computes the compressibility (d(rho)/d(mu)), an easier-to-calculate "stand-in" for conductivity.