The paper by Calabrese and Cardy systematically studies entanglement entropy in relativistic quantum field theory. The entanglement entropy is defined as the von Neumann entropy corresponding to the reduced density matrix of a subsystem \( A \). For a 1+1-dimensional critical system with central charge \( c \), the authors rederive the result \( S_A \sim (c/3) \log \ell \) for a finite interval of length \( \ell \) in an infinite system and extend it to various other cases, including finite systems, finite temperatures, and subsystems consisting of multiple disjoint intervals. For a system away from its critical point, where the correlation length \( \xi \) is large but finite, they show that \( S_A \sim \mathcal{A}(c/6) \log \xi \), where \( \mathcal{A} \) is the number of boundary points of \( A \). These results are verified for a free massive field theory and confirmed for integrable lattice models such as the Ising and XXZ models using corner transfer matrix methods. The free-field results are extended to higher dimensions, leading to a scaling form for the singular part of the entanglement entropy near a quantum phase transition. The paper also discusses the entropy in non-critical 1+1-dimensional models and provides explicit calculations for the transverse Ising chain and the uniaxial XXZ Heisenberg model, demonstrating the consistency of the derived formulas.The paper by Calabrese and Cardy systematically studies entanglement entropy in relativistic quantum field theory. The entanglement entropy is defined as the von Neumann entropy corresponding to the reduced density matrix of a subsystem \( A \). For a 1+1-dimensional critical system with central charge \( c \), the authors rederive the result \( S_A \sim (c/3) \log \ell \) for a finite interval of length \( \ell \) in an infinite system and extend it to various other cases, including finite systems, finite temperatures, and subsystems consisting of multiple disjoint intervals. For a system away from its critical point, where the correlation length \( \xi \) is large but finite, they show that \( S_A \sim \mathcal{A}(c/6) \log \xi \), where \( \mathcal{A} \) is the number of boundary points of \( A \). These results are verified for a free massive field theory and confirmed for integrable lattice models such as the Ising and XXZ models using corner transfer matrix methods. The free-field results are extended to higher dimensions, leading to a scaling form for the singular part of the entanglement entropy near a quantum phase transition. The paper also discusses the entropy in non-critical 1+1-dimensional models and provides explicit calculations for the transverse Ising chain and the uniaxial XXZ Heisenberg model, demonstrating the consistency of the derived formulas.