tb-mean-field-hubbard

Python library to perform tight-binding mean field Hubbard calculations on the conjugated π-networks of organic systems. Only carbon atoms are supported and each atom is modelled by a single p_z orbital hosting a single electron.

The modelled Hamiltonian is the following:

where c^†, c and n are respectively the creation, annihiliation and number operators, t is the hopping integral and U denotes the on-site Coulomb repulsion.

System requirements

Python 3 (tested with 3.6 - 3.9) environment is required with the following libraries (parenthesis indicate tested versions; but the library should work with all recent versions):

• Standard python libraries: numpy (1.17.2), scipy (1.3.1), matplotlib (3.2.1)
• Atomistic simulation environment: ase (3.18.1)
• Python Tight Binding: pythtb (1.7.2)

Note: the dependencies will be automatically installed via pip.

Installation

Option 1) Install the library and dependencies hosted on PyPI:

pip install tb-mean-field-hubbard

Option 2) Manual installation, such that you have direct access to the code and the notebook:

git clone https://github.com/eimrek/tb-mean-field-hubbard.git
cd tb-mean-field-hubbard
pip install -e .

On a normal desktop computer, installation of the python dependencies can take some minutes, while the tb-mean-field-hubbard should install in seconds.

Example usage

Example jupyter notebook example.ipynb is provided that performs the calculation for the Clar's goblet molecule. The geometry is read from a xyz file. The whole notebook should run in a matter of seconds on a normal desktop computer. The following image demonstrates a selection of the output for the calculation for parameters t=2.7 and U=3.0 (both in electronvolts).

In addition to the structure of Clar's goblet, the geom/ folder contains input geometries for triangulene, 4- and 5-rhombene, and several other systems.