Collection of tools for condensed matter physics written in Python.

⚠️ WARNING: This project is still under development and might contain errors or change significantly in the future!

Install via pip from github:

pip install git+https://github.com/dylanljones/cmpy.git@VERSION

or download/clone the package, navigate to the root directory and install via

pip install .

Collection of common condensed matter models (unstable, might change significantly)

A Basis object can be initalized with the number of sites in the (many-body) system:

from cmpy import Basis
basis = Basis(num_sites=3)

The corresponding states of a particle sector can be obtained by calling:

sector = basis.get_sector(n_up=1, n_dn=1)

If no filling for a spin-sector is passed all possible fillings are included. The labels of all states in a sector can be created by the state_labels method:

>>> sector.state_labels()
['..⇅', '.↓↑', '↓.↑', '.↑↓', '.⇅.', '↓↑.', '↑.↓', '↑↓.', '⇅..']

The states of a sector can be iterated by the states-property. Each state consists of an up- and down-SpinState:

state = list(sector.states)[0]
up_state = state.up
dn_state = state.dn

Each SpinState provides methods for optaining information about the state, for example:

>>> up_state.binstr(width=3)
001
>>> up_state.n
1
>>> up_state.occupations()
[1]
>>> up_state.occ(0)
1
>>> up_state.occ(1)
0
>>> up_state.occ(2)
0

The operators-module provides the base-class LinearOperator based on scipy.LinearOperator. A simple sparse implementation of a Hamiltonian is also included.

from cmpy import HamiltonOperator

size = 5
rows = [0, 1, 2, 3, 4, 0, 1, 2, 3, 1, 2, 3, 4]
cols = [0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 1, 2, 3]
data = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]
indices = (rows, cols)
hamop = HamiltonOperator(size, data, indices)

Converting the operator to an array yields

>>> hamop.array()
[[0 1 0 0 0]
 [1 0 1 0 0]
 [0 1 0 1 0]
 [0 0 1 0 1]
 [0 0 0 1 0]]

Many-Body Hamiltonian matrices can be constructed by projecting the elements onto a basis sector. First, the basis and matrix array have to be initialized:

import numpy as np
from cmpy import Basis

basis = Basis(num_sites=2)
sector = basis.get_sector()  # Full basis
ham = np.zeros((sector.size, sector.size))

The Hubbard Hamiltonian, for example, can then be constructed as follows:

from cmpy import project_hubbard_inter, project_hopping

up_states = sector.up_states
dn_states = sector.dn_states

# Hubbard interaction
for i, j, val in project_hubbard_inter(up_states, dn_states, u=[2.0, 2.0]):
    ham[i, j] += val

# Hopping term
for i, j, val in project_hopping(up_states, dn_states, site1=0, site2=1, hop=1.0):
    ham[i, j] += val