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The quantum renormalization group method is applied to study the quantum criticality and entanglement entropy of the ground state of the Ising chain in the presence of antisymmetric anisotropic couplings and alternating exchange interactions. The quantum phase transitions can be characterized by the discontinuity in the second derivative of the energy of renormalized ground state. The phase diagram is obtained by the critical boundary line. The first derivative of entanglement entropy also diverges at the same critical points after enough iterations of the renormalization of coupling constants. The antisymmetric anisotropy and alternating interaction can enhance the renormalized entanglement via the creation of quantum fluctuations. The scaling behavior of the derivative of the entropy around the critical points manifest the logarithm dependence on the size of the spin system.

Quantum renormalization of entanglement in an antisymmetric anisotropic and bond-alternating spin system