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https://github.com/dylanljones/exactdiag

Exact diagonalization of fermionic (many-body) systems
https://github.com/dylanljones/exactdiag

exact-diagonalization greens-functions lehmann-representation physics

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Exact diagonalization of fermionic (many-body) systems

Host: GitHub
URL: https://github.com/dylanljones/exactdiag
Owner: dylanljones
License: mit
Created: 2022-05-04T10:57:45.000Z (over 2 years ago)
Default Branch: master
Last Pushed: 2024-08-05T21:16:11.000Z (3 months ago)
Last Synced: 2024-10-07T10:08:03.798Z (about 1 month ago)
Topics: exact-diagonalization, greens-functions, lehmann-representation, physics
Language: Python
Homepage:
Size: 187 KB
Stars: 2
Watchers: 1
Forks: 0
Open Issues: 1
Metadata Files:
- Readme: README.md
- License: LICENSE

Awesome Lists containing this project

README

        # Exact diagonalization

[![Tests][tests-badge]][tests-url]

[![License: MIT][license-badge]][license-url]

[![Code style: black][black-badge]][black-url]

|⚠️|  This project is still under heavy development and might contain bugs or have breaking API changes in the future. |

|----|:------------------------------------------------------------------------------------------------------------------|

## 🔧 Installation

Install via `pip` from github:

```commandline

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

```

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

````commandline

pip install .

````

## 🚀 Quick-Start

### Basis

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

````python

import exactdiag as ed

basis = ed.Basis(num_sites=3)

````

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

````python

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:

````python

>>> sector.state_labels()

['..⇅', '.↓↑', '↓.↑', '.↑↓', '.⇅.', '↓↑.', '↑.↓', '↑↓.', '⇅..']

````

The states of a sector can be iterated by the ``states``-property.

Each state consists of an up- and down-``SpinState``:

````python

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:

`````python

>>> 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

`````

### Operators

The ``operators``-module provides the base-class ``LinearOperator`` based on ``scipy.LinearOperator``.

A simple sparse implementation of a Hamiltonian is also included.

````python

import exactdiag as ed

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 = ed.HamiltonOperator(size, data, indices)

````

Converting the operator to an array yields

````python

>>> 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 has to be initialized:

````python

import exactdiag as ed

basis = ed.Basis(num_sites=2)

sector = basis.get_sector()  # Full basis

````

The Hubbard Hamilton-operator, for example, can then be constructed as follows:

````python

def hubbard_hamiltonian_data(sector):

    up_states = sector.up_states

    dn_states = sector.dn_states

    # Hubbard interaction

    yield from ed.project_hubbard_inter(up_states, dn_states, u=[2.0, 2.0])

    # Hopping between sites 0 and 1

    yield from ed.project_hopping(up_states, dn_states, site1=0, site2=1, hop=1.0)

rows, cols, data = list(), list(), list()

for i, j, val in hubbard_hamiltonian_data(sector):

    rows.append(i)

    cols.append(j)

    data.append(val)

hamop = ed.HamiltonOperator(sector.size, data, (rows, cols))

````

### Models

Some methods require a model object to work. Users can define their own

models or use one of the following included models:

| Module     | Description                                         | Lattice support    |

|:-----------|:----------------------------------------------------|:-------------------|

| abc        | Model-Parameter container and abstract base classes | -                  |

| anderson   | Anderson impurity models                            | :x:                |

| hubbard    | Hubbard model                                       | :heavy_check_mark: |              |

A custom model can be defined by inheriting from the abstract base classes.

Many-body models, for example, have to implement the `_hamiltonian_data` method,

which generates the rows, columns and values of the Hamilton operator for each

basis sector:

````python

import exactdiag as ed

class CustomModel(ed.models.AbstractManyBodyModel):

    def __init__(self, num_sites, eps=0.0, ...):

        super().__init__(num_sites, eps=eps, ...)

    def _hamiltonian_data(self, up_states, dn_states):

        yield from ed.project_onsite_energy(up_states, dn_states, self.eps)

        ...

````

The Hamilton operator can then be acessed for the full basis or a specific sector

in operator or matrix representation:

````python

model = ed.models.HubbardModel(num_sites=2, neighbors=[[0, 1]], inter=2)

# Sector n↑=1, n↓=1

hamop = model.hamilton_operator(n_up=1, n_dn=1)

# Full basis

sector = model.basis.get_sector()

ham = model.hamiltonian(sector=sector)

ed.matshow(ham, ticklabels=sector.state_labels(), values=True)

````



  



### Green's function

Using a custom defined model or one of the included models the one-particle

(many-body) Green's function can be computed, for example using the Lehmann sum:

````python

import numpy as np

import exactdiag as ed

model = ed.models.HubbardModel.chain(num_sites=7, inter=4.0, beta=10.0).hf()

z = np.linspace(-8, +8, 1001) + 1e-1j

gf = ed.gf_lehmann(model, z, i=3, sigma=ed.UP)[0]

````



  



[tests-badge]: https://img.shields.io/github/actions/workflow/status/dylanljones/exactdiag/test.yml?branch=master&label=test&logo=github&style=flat

[license-badge]: https://img.shields.io/github/license/dylanljones/exactdiag?color=lightgrey&style=flat-square

[black-badge]: https://img.shields.io/badge/code%20style-black-000000.svg?style=flat-square

[license-url]: https://github.com/dylanljones/exactdiag/blob/master/LICENSE

[black-url]: https://github.com/psf/black

[tests-url]: https://github.com/dylanljones/exactdiag/actions/workflows/test.yml