Quantum renormalization group of XY model in two dimensions

Abstract

We investigate entanglement and quantum phase transition (QPT) in a two-dimensional Heisenberg anisotropic spin-1/2 XY model, using quantum renormalization group method (QRG) on a square lattice of $N\times N$ sites. The entanglement through geometric average of concurrences is calculated after each step of the QRG. We show that the concurrence achieves a non zero value at the critical point more rapidly as compared to one-dimensional case. The relationship between the entanglement and the quantum phase transition is studied. The evolution of entanglement develops two saturated values corresponding to two different phases. We compute the first derivative of the concurrence, which is found to be discontinuous at the critical point $\gamma =0$, and indicates a second-order phase transition in the spin system. Further, the scaling behaviour of the system is investigated by computing the first derivative of the concurrence in terms of the system size.

References in corpus (4)

• Entanglement and factorized ground states in two-dimensional quantum antiferromagnets
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Phase Diagram of the One Dimensional $S=1/2$ $XXZ$ model with Ferromagnetic nearest-neighbor and Antiferromagnetic next-nearest neighbor interactions
• Quantum Entanglement in the S=1/2 Spin Ladder with Ring Exchange

Cited by in corpus (2)

• Renormalization of trace distance and multipartite entanglement close to the quantum phase transitions of one- and two-dimensional spin-chain systems
• Scaling of quantum correlation and monogamy relation near a quantum phase transitions in two-dimensional XY spin system