Local relevant deformations are an important tool to study universal properties of quantum critical points. We investigate the effect of small relevant deformations on the bipartite entanglement entropy at the quantum critical points. Within the quantum critical region, a universal power-law correction in the entanglement entropy induced by the relevant operator is found in both one- and two-dimensional critical lattice models. The exponent of the power-law correction term is determined by the scaling dimension of the relevant operator. Based on numerical simulations and scaling theory argument, it is conjectured that such a universal power-law correction in the entanglement entropy is universal for Lorentz invariant quantum critical points. Without Lorentz invariance, it is found the exponent in the power-law correction term does not fit in with the scaling argument in models with a dynamical exponent $z=2$ in two dimensions. This may be because the relevant operator added in the lattice model corresponds to complicated operators in the corresponding conformal field theory. Our study provides a different perspective to extract universal information of quantum critical points. We expect it would be useful to detect unique properties of topological quantum phase transitions.

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• Critical phenomena
• Entropy
• Quantum phase transitions