In this paper the the effect of Dzyaloshinskii-Moriya interaction and anisotropy on the Entanglement of Heisenberg model has been studied. While the anisotropy suppress the entanglement due to favoring of the alignment of spins, the DM interaction restore the spoiled entanglement via the introduction of the quantum fluctuations. Thermodynamic limit of the model and emerging of nonanalytic behavior of the entanglement have also been probed. The singularities of the entanglement correspond to the critical boundary separating different phases of the model. The effect of gapped and gapless phases of the model on the features of the entanglement has also been discussed.

We have studied the phase diagram and entanglement of the one dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has two phases, antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of new spin operators which are defined by a nonlocal transformation. PACS numbers: 75.10.Pq, 73.43.Nq, 03.67.Mn, 64.60.ae J J J J J J J J ' J ' J effWe have considered the three-site block (Fig.(1)) with the following Hamiltonian

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.

We have combined the idea of renormalization group and quantum information theory. We have shown how the entanglement or concurrence evolve as the size of the system being large, i.e. the finite size scaling is obtained. Moreover, It introduces how the renormalization group approach can be implemented to obtain the quantum information properties of a many body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent which is directly associated with the divergence of the correlation length.A fundamental difference between quantum and classical physics is the possible existence of nonclassical correlations in quantum systems called Entanglement 1 . Recently, the study of strongly correlated systems in condensed matter physics from the perspective notions of quantum information theory has been received much attentions. It seems that the main motivations for such treatment are two folds: (i) Over the last decade the entanglement has been realized to be a crucial resource to process and send information in novel ways such as quantum teleportation, supercoding and algorithms for quantum computations 2 , (ii) the novel features of the ground state of many body systems which consists of a superposition of huge number of product states opens the question of how this states are interrelated.The role of entanglement in quantum phase transition (QPT) 3 is of considerable interest 4 . Quantum phase transitions occur at absolute zeroand are driven by quantum fluctuations. Entanglement as a direct measure of quantum correlations shows nonanalytic behavior such as discontinuity in the vicinity of the quantum phase transition point 5 . In the past few years the subject of several activities were to investigate the behavior of entanglement in the vicinity of quantum critical point for different spin models 4,6,7,8,9,10 as well as itinerant systems 11,12,13 .Our main purpose in this work is to combine the idea of quantum renormalization group 14,15 and quantum information theory. This will give two insights on (i) how a quantum information property (QIP) evolves as the size of system becomes large and (ii) QRG connects the nonanalytic behavior of entanglement to the critical phenomenon properties of the model. To have a concrete discussion, the one dimensional S = 1 2 Ising model in a transverse field (ITF) has been considered by implementing the quantum renormalization group (QRG) approach.The main idea of the RG method is the mode elimina-tion or thinning of the degrees of freedom followed by an iteration which reduces the number of variables step by step until reaching a fixed point. In Kadanoff's approach, the lattice is divided into blocks. Each block is treated independently to build the projection operator onto the lower energy subs...

One dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces the gap in the spectrum of the model with easy-plain anisotropy. Using conformal invariance the field dependence of the gap at small fields is found. The ground state phase diagram is obtained. It contains four phases with different types of the long range order (LRO) and a disordered one. These phases are separated by critical lines, where the gap and the long range order vanish. Using scaling estimations and a mean-field approach as well as numerical calculations in the vicinity of all critical lines we found the critical exponents of the gap and the LRO. It is shown that transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model. 75.10.Jm -Quantized spin models