Erratum: Quantum renormalization group of theXYmodel in two dimensions [Phys. Rev. A92, 032327 (2015)]

Abstract

There is a typing mistake in the expression of γ 4 given in the Appendix. The actual expression is γ (5+α 1 +γ 2) 2 √ 2α 2 , which is used in the calculations throughout the paper. In the caption of Fig. 6, "(see Fig. 6)" should read "(see Fig. 4)".

Spatial dependence of entanglement renormalization in XY model

“…It reaches to maximum value at the critical point and it can be seen that this maximum value is smaller in three dimensions as compared to its two-dimensional counterpart. Likewise scenario can be seen for the qualitative and the quantitative behavior of the concurrence in the XY model, as we go from the lower to higher dimensions [10,31]. It is the monogamy that limits the entanglement shared among the number of neighbor sites [19].…”

“…1.) to obtain the effective Hamiltonian which has similar structure as that of the original Hamiltonian. From the previous studies of the XY model [10,11,31], it is found that in the renormalization process, the projection operator constructed from the degenerate ground states of the block works well for obtaining the effective Hamiltonian in the renormalized Hilbert space of spin -1/2 particle. The degenerate ground eigenstates can only be obtained if we consider the blocks containing odd number of spins in any spatial dimensions.…”

“…Similarly, the symmetry of the Hamiltonian predicts that the magnitude of the entanglement may further reduce in three dimensions due to increase in the interactions. Moreover, the monogamy is responsible for achieving the critical point more rapidly, as less QRG iterations are required in higher dimensions [31]. This critical phenomenon is described by the behavior of the ground state entanglement as the system size increases.…”

“…The study of quantum correlations in the spin systems through the QRG reflects both quantum information properties as well as critical properties of the system [5,6,10,29,[31][32][33]. The ground-state spin entanglement in ddimensional bipartite lattice of the XXZ moel is studied [34], where bipartite concurrence shows similar qualitative behavior.…”

“…Recently, we extended the application of Kadanoffs block approach from the one dimension to the two dimensional Hisenberg XY model [31] . From the previous study [31], we realize that the symetrical extension to the three-dimensional spin system is quite possible and is presented here. Where we developed the two-dimensional five-spins Kadanoff block from the one-dimensional three-spins kadanoff block.…”