https://github.com/twesterhout/lattice-symmetries

A package to simplify working with symmetry-adapted quantum many-body bases. Provides a good foundation for writing custom exact diagonalization and variational Monte Carlo software
https://github.com/twesterhout/lattice-symmetries

bit-manipulation c cpp17 exact-diagonalization lattice-symmetries many-body-physics neural-network permutation quantum-mechanics symmetries symmetry-groups

Last synced: 13 days ago
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A package to simplify working with symmetry-adapted quantum many-body bases. Provides a good foundation for writing custom exact diagonalization and variational Monte Carlo software

• Host: GitHub
• URL: https://github.com/twesterhout/lattice-symmetries
• Owner: twesterhout
• License: bsd-3-clause
• Created: 2020-08-12T20:50:30.000Z (about 4 years ago)
• Default Branch: master
• Last Pushed: 2024-10-26T20:05:27.000Z (13 days ago)
• Last Synced: 2024-10-26T22:10:22.060Z (13 days ago)
• Topics: bit-manipulation, c, cpp17, exact-diagonalization, lattice-symmetries, many-body-physics, neural-network, permutation, quantum-mechanics, symmetries, symmetry-groups
• Language: Haskell
• Homepage:
• Size: 6.24 MB
• Stars: 29
• Watchers: 6
• Forks: 8
• Open Issues: 9
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
> ⚠️ **INFO**

>

> This is a Haskell rewrite of the original

> [lattice-symmetries](https://github.com/twesterhout/lattice-symmetries). At

> some point, this package will completely replace the first version of

> lattice-symmetries.

# lattice-symmetries [![Build](https://github.com/twesterhout/lattice-symmetries-haskell/actions/workflows/ci.yml/badge.svg)](https://github.com/twesterhout/lattice-symmetries-haskell/actions/workflows/ci.yml)

[![License](https://img.shields.io/badge/License-BSD%203--Clause-blue.svg)](https://opensource.org/licenses/BSD-3-Clause)

A package to simplify working with symmetry-adapted quantum many-body bases.

## Hamiltonians

#### Spins

MathsCode

$$

\mathbf{S}_i \cdot \mathbf{S}_j = S^x_i S^x_j + S^y_i S^y_j + S^z_i S^z_j

$$

`"Sˣ₀ Sˣ₁ + Sʸ₀ Sʸ₁ + Sᶻ₀ Sᶻ₁"`

or

`"Sx0 Sx0 + Sy1 Sy1 + Sz0 Sz1"`

$$

\mathbf{S}_i \cdot \mathbf{S}_j = \frac{1}{4} \left( \sigma^x_i \sigma^x_j + \sigma^y_i \sigma^y_j + \sigma^z_i \sigma^z_j \right)

$$

`"0.25 (σˣ₀ σˣ₁ + σʸ₀ σʸ₁ + σᶻ₀ σᶻ₁)"`

$$

\sigma^{+}_i \sigma^{-}_j

$$

`"σ⁺₀ σ⁻₁"` or

`"\sigma^+_0 \sigma^-_1"` or

`"\sigma+0 \sigma-1"`

#### Electrons

MathsCode

$$

c^\dagger_{i\uparrow}c_{j\uparrow} + c^\dagger_{i\downarrow}c_{j\downarrow}

$$

`"c†₀↑ c₁↑ + c†₀↓ c₁↓"`

$$

n_{i\uparrow} n_{i\downarrow}

$$

`"n₀↑ n₀↓"` or

`"n0up n0down"`