This paper explores the role of entanglement in quantum critical phenomena, focusing on how ground-state entanglement scales with system size near and at quantum critical points in one-dimensional spin chain models. The authors use the von Neumann entropy of the reduced density matrix to quantify entanglement, finding that it scales logarithmically with the size of the block of spins, with a coefficient related to the central charge of the conformal field theory describing the quantum phase transition. This result shows that entanglement obeys universal scaling laws dictated by the conformal group, and that the entanglement entropy diverges logarithmically at critical points, consistent with the behavior of geometric entropy in conformal field theory. The study considers two models: the XY model and the XXZ model. For the XY model, the authors derive an analytical expression for the entanglement entropy in the thermodynamic limit, finding that it scales as $ \frac{1}{3}\log_{2}(L) + k_{1}(a) $ for the XX model and $ \frac{1}{6}\log_{2}(L) + k_{2} $ for the Ising model. For the XXZ model, they use the Bethe ansatz to compute the entanglement entropy for small systems, finding that it exhibits a logarithmic divergence at critical points, consistent with the central charge of the underlying conformal field theory. The results show that non-critical ground states have entanglement entropy that either vanishes or grows monotonically with system size, while critical ground states exhibit a logarithmic divergence in entanglement entropy. This behavior is consistent with the conformal field theory description of quantum phase transitions, and the authors argue that the entanglement entropy provides a measure of the criticality of the system. The study also highlights the connection between entanglement and the renormalization group flow, showing that entanglement decreases along the flow, consistent with Zamolodchikov's c-theorem. The authors also find that the entanglement entropy satisfies a majorization relation, which is a signature of conformal invariance. The results have implications for the understanding of quantum critical phenomena and the role of entanglement in quantum information science.This paper explores the role of entanglement in quantum critical phenomena, focusing on how ground-state entanglement scales with system size near and at quantum critical points in one-dimensional spin chain models. The authors use the von Neumann entropy of the reduced density matrix to quantify entanglement, finding that it scales logarithmically with the size of the block of spins, with a coefficient related to the central charge of the conformal field theory describing the quantum phase transition. This result shows that entanglement obeys universal scaling laws dictated by the conformal group, and that the entanglement entropy diverges logarithmically at critical points, consistent with the behavior of geometric entropy in conformal field theory. The study considers two models: the XY model and the XXZ model. For the XY model, the authors derive an analytical expression for the entanglement entropy in the thermodynamic limit, finding that it scales as $ \frac{1}{3}\log_{2}(L) + k_{1}(a) $ for the XX model and $ \frac{1}{6}\log_{2}(L) + k_{2} $ for the Ising model. For the XXZ model, they use the Bethe ansatz to compute the entanglement entropy for small systems, finding that it exhibits a logarithmic divergence at critical points, consistent with the central charge of the underlying conformal field theory. The results show that non-critical ground states have entanglement entropy that either vanishes or grows monotonically with system size, while critical ground states exhibit a logarithmic divergence in entanglement entropy. This behavior is consistent with the conformal field theory description of quantum phase transitions, and the authors argue that the entanglement entropy provides a measure of the criticality of the system. The study also highlights the connection between entanglement and the renormalization group flow, showing that entanglement decreases along the flow, consistent with Zamolodchikov's c-theorem. The authors also find that the entanglement entropy satisfies a majorization relation, which is a signature of conformal invariance. The results have implications for the understanding of quantum critical phenomena and the role of entanglement in quantum information science.