The paper investigates the entanglement asymmetry in one-dimensional critical systems described by conformal field theories (CFTs), focusing on its relation to non-topological defects. Entanglement asymmetry is an information-based observable that quantifies the degree of symmetry breaking in a quantum system. The analysis is formulated in terms of partition functions on Riemann surfaces with non-topological defect lines inserted at their branch cuts. For large subsystems, these partition functions are determined by the scaling dimension of the defects, leading to the observation that entanglement asymmetry acquires a subleading contribution scaling as log(ℓ)/ℓ for large subsystem length ℓ. As an illustrative example, the paper considers the XY spin chain, which is described by the massless Majorana fermion theory at criticality. The corresponding defect is marginal, and the scaling dimension of these defects is related to the ground state energy of the massless Majorana fermion on a circle with equally-spaced point defects. Using conformal invariance, the paper derives the exact expression for the scaling dimension associated with n defects of arbitrary strengths, generalizing a known formula for the n=1 case. This result is then used to derive the exact prefactor of the log(ℓ)/ℓ term in the asymmetry of the critical XY chain. The paper also discusses the asymptotic behavior of the entanglement asymmetry, showing that it exhibits a fundamentally distinct behavior compared to entanglement entropy. The entanglement asymmetry is shown to be non-negative and vanishes if and only if the subsystem is in a symmetric state. The paper provides a detailed analysis of the entanglement asymmetry in the ground state of the XY spin chain, using both analytical and numerical methods. The results are applied to the critical XY spin chain, where the entanglement asymmetry is found to exhibit a log(ℓ)/ℓ term, which is absent in non-critical systems. The paper concludes that the entanglement asymmetry provides a powerful tool for studying symmetry breaking in quantum systems, particularly in critical systems.The paper investigates the entanglement asymmetry in one-dimensional critical systems described by conformal field theories (CFTs), focusing on its relation to non-topological defects. Entanglement asymmetry is an information-based observable that quantifies the degree of symmetry breaking in a quantum system. The analysis is formulated in terms of partition functions on Riemann surfaces with non-topological defect lines inserted at their branch cuts. For large subsystems, these partition functions are determined by the scaling dimension of the defects, leading to the observation that entanglement asymmetry acquires a subleading contribution scaling as log(ℓ)/ℓ for large subsystem length ℓ. As an illustrative example, the paper considers the XY spin chain, which is described by the massless Majorana fermion theory at criticality. The corresponding defect is marginal, and the scaling dimension of these defects is related to the ground state energy of the massless Majorana fermion on a circle with equally-spaced point defects. Using conformal invariance, the paper derives the exact expression for the scaling dimension associated with n defects of arbitrary strengths, generalizing a known formula for the n=1 case. This result is then used to derive the exact prefactor of the log(ℓ)/ℓ term in the asymmetry of the critical XY chain. The paper also discusses the asymptotic behavior of the entanglement asymmetry, showing that it exhibits a fundamentally distinct behavior compared to entanglement entropy. The entanglement asymmetry is shown to be non-negative and vanishes if and only if the subsystem is in a symmetric state. The paper provides a detailed analysis of the entanglement asymmetry in the ground state of the XY spin chain, using both analytical and numerical methods. The results are applied to the critical XY spin chain, where the entanglement asymmetry is found to exhibit a log(ℓ)/ℓ term, which is absent in non-critical systems. The paper concludes that the entanglement asymmetry provides a powerful tool for studying symmetry breaking in quantum systems, particularly in critical systems.