Erratum: Von Neumann entropy and bipartite number fluctuation in quantum phase transitions [Phys. Rev. B 83,113104 (2011)]

摘要

In our paper, Fig. 1 of the von Neumann entropy S versus the coupling parameter V is incorrect. The ground state |Ψ_0> was written as a linear combination of the basesrn|Ψ_0) =∑_ia_i|i＞rn= ∑a_ic_i_1~+c_i_2~+....c_i_m~†|0＞rn=∑_ia_i(-1)~Pc_j_1~†.....c_j_M_A~†c_k_1~†c_M_B~+|0＞rnwhere we bipartite the system into even and odd subsystems by reordering the creation operators as j_1 <...< J_m_a are even, k_1＜...＜ k_M_B are odd, and M_A + M_b = M. In the previous calculation, the error originated in neglecting the sign (-l)~P. Figure 1 in the paper should be replaced by the corrected Fig. 1 here. The entropy in quantum phase transitions plays the role of order parameter in thermal phase transitions, for instance, magnetization in the Ising model.