---

DMRG Implementation

This repository contains implementations of the Density-Matrix Renormalization Group (DMRG) algorithm, along with supporting code for numerical simulations of quantum many-body systems. The project is designed to provide pedagogical insights into DMRG concepts and includes Python and Julia implementations.

---

Contents

• DMRG_python.ipynb: A Jupyter Notebook showcasing the DMRG algorithm in Python with detailed explanations and visualizations.
• dmrg.jl: A Julia implementation of the DMRG algorithm for high-performance computations.
• python_code_without_dmrg.py: Auxiliary Python code for quantum systems without explicit DMRG implementation.
• README.md: Documentation for the project.

---

Features

• Implementation of the DMRG algorithm for 1D quantum systems.
• Support for spin chain models (e.g., Heisenberg model).
• Visualization of entanglement entropy and energy convergence.
• Modular code structure for easy extension to other models.

---

Requirements

Python Environment:

• Python 3.8+
• Required packages:
  • numpy
  • matplotlib
  • scipy

Julia Environment:

• Julia 1.9+
• Required packages:
  • LinearAlgebra
  • Plots

---

Installation

1. Clone this repository:

   git clone https://github.com/yourusername/DMRG-project.git
   cd DMRG-project

2. Install dependencies:
   • For Python:

     pip install numpy matplotlib scipy

   • For Julia:

     using Pkg
     Pkg.add("LinearAlgebra")
     Pkg.add("Plots")

---

Usage

Python Implementation:

Run the Jupyter Notebook DMRG_python.ipynb to explore step-by-step explanations and results:

jupyter notebook DMRG_python.ipynb

Julia Implementation:

Execute the dmrg.jl file directly in Julia to run the DMRG algorithm on predefined models:

julia dmrg.jl

Auxiliary Code:

Use python_code_without_dmrg.py for additional computations or as a starting point for custom implementations.

---

Examples

1. Heisenberg Spin Chain:

   • Compute ground state energy using DMRG.
   • Visualize entanglement entropy across iterations.

2. Custom Hamiltonians:

   • Modify the Hamiltonian in either Python or Julia scripts to study other quantum systems.

---

Acknowledgments

This project is inspired by pedagogical resources on DMRG and tensor networks, including works by Steven White and Ulrich Schollwöck.

---