Renormalization of entanglement in the anisotropic Heisenberg(XXZ)model

Abstract

We have applied our recent approach (Kargarian, et.al Phys. Rev. A 76, 60304 (R) (2007)) to study the quantum information properties of the anisotropic s=1/2 Heisenberg chain. We have investigated the underlying quantum information properties like the evolution of concurrence, entanglement entropy, nonanalytic behaviours and the scaling close to the quantum critical point of the model. Both the concurrence and the entanglement entropy develop two saturated values after enough iterations of the renormalization of coupling constants. This values are associated with the two different phases, i.e Néel and spin liquid phases. The nonanalytic behaviour comes from the divergence of the first derivative of both measures of entanglement as the size of system becomes large. The renormalization scheme demonstrates how the minimum value of the first derivative and its position scales with an exponent of the system size. It is shown that this exponent is directly related to the critical properties of the model, i.e. the exponent governing the divergence of the correlation length close to the quantum critical point. We also use a renormalization method based on the quantum group concept in order to get more insight about the critical properties of the model and the renormalization of entanglement.

Entanglement and quantum phase transition in the one-dimensional anisotropicXYmodel

“…The pairwise entanglement of the system is also discussed by means of quantum renormalization group (QRG) method [16,17]. Very recently, the spin−1/2 Ising and Heisenberg models are studied by using the same method by a group of Iran and found that the systems exist QPT [18][19][20][21]. It is also shown that the nonanalytic behavior of the entanglement and the scaling behaviors closing to the quantum critical point are obtained.…”

Quantum phase transitions in the Kondo-necklace model: perturbative continuous unitary transformation approach

“…In the current work, we consider the thermodynamic limit via PCUT and probe phase transitions in spatial dimensions d = 1, 2, and 3. Despite its local nature, nonanalytic behavior of derivatives of concurrence signals a phase transition in the system, and its scaling in the vicinity of critical points is connected to the universality class of the model [19][20][21] . We will show that concurrence does not capture the critical properties of the KN model at the mentioned spatial dimensions, manifesting that the underlying correlations are not of the bipartite nature.…”

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

“…In 2002, A. Osterloh et al first introduced the density matrix renormalization-group (DMRG) approach to study the entanglement close to the quantum phase transition (QPT) [20] and reveal a profound difference between classical correlations and the non-local quantum correlation. 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].…”