This project is about plotting various standard properties of 2-dimensional tight-binding hamiltonians.

Keywords: computational condensed matter physics, Fermi surface, tight binding approximation, energy bands, cuprates, two-dimensional systems, many body physics

Due to tkinter dependency for plotting, using a conda environment is preferred. Install miniconda: https://docs.conda.io/en/latest/miniconda.html Then create a conda environment like:

conda env create -f ./conda_environment.yml
conda env activate fermi

import warnings
warnings.filterwarnings('ignore')
from tba import *
x = CuprateSingleBand()
x.plot_bands()
x.plot_Fermi_surface_contour()
x.filling_vs_energy()
# calculate charge susceptibility \chi_c
x.chic.plot_vs_q()

The following references are recommended for topics discussed in this repository:

• Piers Coleman, Introduction to Many Body Physics, 2015, Cambridge University Press
• Ashcroft & Mermin, Solid State Physics

Notation basics

Energy bands, Fermi Surface, Density of States

Susceptibility

Random Phase Approximation (RPA)

Generalized RPA (gRPA)

Cuprate Single Band

Cuprate Three Band

Cuprate Four Band LCO

D-density-wave (DDW)

Tetra Single Band Superconductor

Hexa Single Band

• Multiband susceptibility
• Adaptive susceptibility plots using python adaptive or scikit-optimize
• Mean field and broken symmetry calculations, and coexisting orders
• improve pytests, documentation etc
• speed up integration via low-level callback functions