Comprehensive study of Entanglement Entropy in Quantum Field Theory: Analysis of Conformal Field Theory to Massive Field Extensions and Holographic Entanglement

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Year : 2025 | Volume : | : | Page : –
    By

    vaidik A sharma,

  • N. Madurai Meenachi2,

  1. Student, Department of Physics ,Birla Institute of Technology, Rajasthan, India
  2. Scientific officer, Indira Gandhi Centre for Atomic Research, Kalpakkam, India

Abstract

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This paper provides an in-depth analysis of entanglement entropy (EE) in quantum field theory (QFT), with a particular focus on its computation using the replica trick and its applications to both conformal and non-conformal systems. Beginning with an introduction to the basics of QFT, the study explains how entanglement entropy quantifies the quantum correlations between subsystems in a pure state, represented by the von Neumann entropy of the reduced density matrix. The replica trick is employed to derive the entanglement entropy, involving path integrals over n-sheeted Riemann surfaces. The paper demonstrates the method’s utility in 1+1-dimensional conformal field theory (CFT), where the central charge governs universal properties of entropy. It further extends the analysis to massive field theories, finite systems, and topological phases, exploring how deviations from conformal symmetry affect entanglement. The work also delves into the AdS/CFT correspondence, showcasing how holographic techniques facilitate entanglement entropy calculations in higher-dimensional systems via the Ryu-Takayanagi formula. In addition, the study investigates entanglement entropy in quantum lattice systems, considering the effects of spatial and thermal fluctuations. Numerical methods are used to compute the scaling of entanglement entropy with interval length for varying system masses and temperatures, highlighting the influence of these parameters on entropy behavior. Fractal lattice structures are explored to uncover unique entropy scaling laws and self-similar entanglement patterns. This study advances the under-standing of EE in diverse quantum systems and establishes a foundation for exploring its role in quantum criticality and fractal geometries. The paper also explores multiscale entanglement entropy (MSE), offering a comprehensive framework for future research in quantum critical phenomena and non-equilibrium systems, shedding light on the complex relationship between quantum entanglement and thermal effects. This work serves as a foundational reference for future theoretical and computational studies in quantum entanglement

Keywords: Entanglement Entropy, Quantum Field Theory, Conformal Field Theory, AdS/CFT Correspondence, Holographic Principle, String Theory, Quantum Gravity

How to cite this article:
vaidik A sharma, N. Madurai Meenachi2. Comprehensive study of Entanglement Entropy in Quantum Field Theory: Analysis of Conformal Field Theory to Massive Field Extensions and Holographic Entanglement. Research & Reviews : Journal of Physics. 2025; ():-.
How to cite this URL:
vaidik A sharma, N. Madurai Meenachi2. Comprehensive study of Entanglement Entropy in Quantum Field Theory: Analysis of Conformal Field Theory to Massive Field Extensions and Holographic Entanglement. Research & Reviews : Journal of Physics. 2025; ():-. Available from: https://journals.stmjournals.com/rrjophy/article=2025/view=0

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Ahead of Print Subscription Review Article
Volume
Received 22/10/2024
Accepted 26/12/2024
Published 07/02/2025
336