Code

Here is some of the code that I have developed for my research. Not uploaded to the internet yet but stay tuned!

Lanczos [coming soon]

C++ code to diagonalize Hermitian matrices using the Lanczos algorithm without re-orthogonalization.

Features

Lightweight template header-only library built on top of Eigen.
Allows user-defined matrix-vector multiplication.
Supports banded Lanczos recursion.

Noodle [coming soon]

(Noo)bie (D)iagonalization: (L)anczos and (E)xact

A simple and easy to implement C++ header-only framework for constructing quantum many-body Hamiltonians. Diagonalizes the Hamiltonian matrix either exactly with Eigen or approximately with Lanczos.

Features

Lightweight template header-only library built on top of Eigen.
Can treat both fermions and bosons.
Compute: excitation spectrums and static & dynamic correlation functions (e.g. specific heat, Green's functions, dynamic structure factor, etc.).

Because Noodle is a general framework, it can treat a wide range of quantum-many-body problems.

So far Noodle has been used for

Fractional quantum Hall effect
- Models: Spinless fermions and bosons on the surface of a sphere with a magnetic monopole at the center and interacting through long range (Coulomb) and short range (Laughlin) interactions. Momentum space.
- Calculation: Excitation spectrums and thermodynamic observables e.g. specific heat, entropy, free-energy.
Fermi-Hubbard models
- Models: 1D, 2D, square lattice, kagome lattice, two-orbital, and checkerboard lattice with complex hoppings. Real space.
- Calculation: Green's function and spin susceptibility.