Entanglement and quantum phase transition in the one-dimensional anisotropicXYmodel

Abstract

In this paper the entanglement and quantum phase transition of the anisotropic s = 1/2 XY model are studied by using the quantum renormalization group method. By solving the renormalization equations, we get the trivial fixed point and the untrivial fixed point which correspond to the phase of the system and the critical point, respectively. Then the concurrence between two blocks are calculated and it is found that when the number of the iterations of the renormalziation trends infinity, the concurrence develops two staturated values which are associated with two different phases, i.e., Ising-like and spin-fluid phases. We also investigate the first derivative of the concurrence, and find that there exists non-analytic behaviors at the quantum critical point, which directly associate with the divergence of the correlation length. Further insight, the scaling behaviors of the system are analyzed, it is shown that how the maximum value of the first derivative of the concurrence reaches the infinity and how the critical point is touched as the size of the system becomes large.

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.…”

“…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.…”

“…Quantum renormalization group (QRG) method is an effective technique in order to address such problems, i.e. analytically in one dimension [5][6][7][8][9][10][11][12][13] and numerically in higher dimensions. In the past, different numerical techniques were used to study such systems [14,15].…”

Thermal entanglement between non-nearest-neighbor spins on fractal lattices

“…Further,by applying the quantum renormalization-group (QRG) approach, M. Kargarian et al investigated the entanglement in the anisotropic Heisenberg model [21,22] and discussed the nonanalytic behaviors and the scaling close to the quantum critical point of the system. Recently We have calculated the block-block entanglement in the XY model without and with staggered Dzyaloshinskii-Moriya (DM) interaction by using this QRG method and have found the DM interaction can enhance the entanglement and influence the QPT of the system [23,24].…”