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Modern Physics Letters B

LEVEL CROSSING AND QUANTUM PHASE TRANSITION OF THE XY RING

Jun Jing, Hongru Ma

Published Mar 30, 2008• 0 citations
Publisher

Abstract

The ground state of a spin-1/2 ring in the Heisenberg XY model is investigated. The spatial correlation and concurrence between an arbitrary nearest-neighbor pair of spins are calculated with different coupling strength, anisotropic parameter and magnitude of the transverse field. Abrupt changes of the correlation and concurrence due to the competition between coupling and alignment are observed. The transition is found to be the direct result of the level crossing of a finite size spin system.

DOI
10.1142/s0217984908015115

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In this paper the entanglement and quantum phase transition of the anisotropic spin-1/21/21/2 XY\mathit{XY}XY model are studied by using the quantum renormalization-group method. By solving the renormalization equations, we get the trivial and nontrivial fixed points, which correspond to the phase of the system and the critical point, respectively. The concurrence between two blocks are calculated and it is found that when the number of iterations of the renormalization tends to infinity, the concurrence develops two saturated values that 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 nonanalytic behaviors at the quantum critical point, which are directly associated with the divergence of the correlation length. To gain further insight, the scaling behaviors of the system are analyzed and it is shown that the maximum value of the first derivative of the concurrence reaches infinity and the critical point is approached as the size of the system increases.