Collection of tools for condensed matter physics written in Python.
| ❗ | Most of the code is beeing migrated to the exactdiag repository and will be removed soon! |
|---|
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 .
| Module | Description |
|---|---|
| basis | Tools for many-body basis representations |
| collection | Collection of helpful methods and constants |
| cpa | Coherent potantial approximation (on-site disorder) |
| disorder | Methods for constructing disorder |
| exactdiag | Exact diagonalization methods |
| greens | Some implementations for the computation of Green's functions |
| matrix | Matrix methods |
| operators | Abstract linear operator, sparse implementation and other tools |
Collection of common condensed matter models (unstable, might change significantly)
| Module | Description | Lattice support |
|---|---|---|
| abc | Model-Parameter container and abstract base classes | - |
| anderson | Anderson imurity models | ❌ |
| ising | Ising model | ✔️ |
| heisenberg | Heisenberg model | ✔️ |
| hubbard | Hubbard model | ❌ |
| tightbinding | Thight-Binding model | ✔️ |
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.dnEach 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)
0The 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