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FuzzifiED : Julia Package for Numerics on the Fuzzy Sphere

Zheng Zhou

TL;DR

This documentation provides a review of the fuzzy sphere regularisation and an instruction for using FuzzifiED for numerical calculations.

Abstract

The Julia package FuzzifiED aims at simplifying the numerical calculations on the fuzzy sphere. It supports exact diagonalisation (ED) and density matrix renormalisation group (DMRG) calculations. FuzzifiED can also apply to generic fermionic and bosonic models. This documentation provides a review of the fuzzy sphere regularisation and an instruction for using FuzzifiED for numerical calculations.

FuzzifiED : Julia Package for Numerics on the Fuzzy Sphere

TL;DR

This documentation provides a review of the fuzzy sphere regularisation and an instruction for using FuzzifiED for numerical calculations.

Abstract

The Julia package FuzzifiED aims at simplifying the numerical calculations on the fuzzy sphere. It supports exact diagonalisation (ED) and density matrix renormalisation group (DMRG) calculations. FuzzifiED can also apply to generic fermionic and bosonic models. This documentation provides a review of the fuzzy sphere regularisation and an instruction for using FuzzifiED for numerical calculations.

Paper Structure

This paper contains 83 sections, 112 equations, 3 tables.

Table of Contents

  1. Purpose and Outline
  2. Review of the Fuzzy Sphere
  3. Introduction
  4. Conformal Field Theory
  5. Fuzzy Sphere
  6. Review of Existing Works
  7. The pioneering work Zhu2022
  8. Accessing Various Conformal Data
  9. OPE coefficients Hu2023Mar
  10. Correlation functions Han2023Jun
  11. Entropic $F$-function Hu2024
  12. Conformal generators Fardelli2024Fan2024
  13. The cross-cap coefficients Dong2025
  14. Developing Techniques to Improve the Numerical Precision
  15. Quantum Monte Carlo on the fuzzy sphere Hofmann2023
  16. ...and 68 more sections