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1D Random Antiferromagnetic Heisenberg Model Simulation

This repository contains the code, thesis, and figures for a numerical simulation of the 1D Random Antiferromagnetic Heisenberg Model using the Real Space Renormalization Group (RSRG) method.

File Structure

.
├── bond_distance.py
├── bond_distribution.py
├── Figures
│   └── Matrix
│       ├── startmatrix.png
│       ├── midrg1.png
│       ├── midrg5.png
│       ├── midrg10.png
│       ├── midrg13.png
│       └── singlet-phase.png
├── matrix_animation.py
├── random_chain.py
├── requirements.txt
└── Thesis
    └── thesis.pdf

Files Description

  • random_chain.py: Contains the Random_chain class, which performs the renormalization group transformations for the 1D random antiferromagnetic Heisenberg model.
  • bond_distance.py: Calculates the distances between the bonds for a given chain length and number of simulations, and plots a Seaborn kdeplot of the distances.
  • bond_distribution.py: Calculates the final bond distribution for a given chain length and plots the bond strengths using a Seaborn kdeplot.
  • matrix_animation.py: Creates a matrix animation of the renormalization group process, saving snapshots of the process in the "Figures/Matrix" folder.
  • requirements.txt: Lists the required packages to run the Python code in this repository.

Folders Description

  • Figures: Contains the output plots and animations generated by the Python scripts. It includes a subfolder Matrix with snapshots of the matrix_animation process.
  • Thesis: Contains the PDF file of the author's thesis.

Thesis

The Thesis folder contains a PDF file of the author's thesis, which provides a detailed explanation of the 1D random antiferromagnetic Heisenberg model and the renormalization group method used in this repository.

Python Code

The main class for the simulation is Random_chain, which can be found in the random_chain.py file. This class initializes the random chain and performs the renormalization steps.

The class has the following methods:

  • __init__(self, bond_number, resc): Constructor that takes the number of bonds as an input. Also includes a resc variable (default = True) so that rescaling is turned off (Rescaling off allows for the bond_distribution to function properly.)
  • matrix_creator(self): Creates the initial bond matrix with random values.
  • bonds(self): Determines the maximum bond value and its indices, as well as the effective bond and the corresponding parameters (zeta, gamma, and eta).
  • decimate(self): Performs the decimation step of the Real Space Renormalization Group (RSRG) method.
  • rescale(self): Performs the rescaling step of the Real Space Renormalization Group (RSRG) method.
  • renormalization(self): Applies the full renormalization (decimation and rescaling) on the chain.

Installation and Usage

To run the Python scripts, first clone this repository and navigate to the project directory:

git clone https://github.com/yourusername/1d-random-antiferromagnetic-heisenberg.git
cd 1d-random-antiferromagnetic-heisenberg`

Next, install the required packages listed in requirements.txt:

pip install -r requirements.txt

Once the required packages are installed, you can run the Python scripts.

Example

from random_chain import Random_chain

# Create a random chain with 100 bonds
chain = Random_chain(100)

# Perform 50 renormalization steps
for _ in range(50):
    chain.renormalization()

# Access the final bond matrix
final_bond_matrix = chain.bond_matrix

# Access the zeta, gamma, and eta parameters
zeta = chain.zeta
gamma = chain.gamma
eta = chain.eta

Dependencies

  • Python 3.x
  • NumPy
  • Matplotlib
  • tqdm
  • Seaborn
  • SciPy

License

This project is licensed under the MIT License.