Entanglement and quantum phase transition in the one-dimensional anisotropic XY model

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.

10 pages, 5 figures

References in corpus (4)

• Quantum Phase Transitions and Bipartite Entanglement
• Entanglement in a second order quantum phase transition
• Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model

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• Decoherence and relaxation of topological states in extended quantum Ising models
• Spotlighting quantum phase transition in spin-1/2 Ising-Heisenberg diamond chain employing Measurement-Induced Nonlocality
• Single-ion anisotropy effects on the critical behaviors of quantum entanglement and correlation in the spin-1 Heisenberg chain
• Exact phase diagram and topological phase transitions of the XYZ spin chain
• Quantum Quench dynamics in XY spin chain with ferromagnetic and antiferromagnetic interactions
• Scaling of quantum correlation and monogamy relation near a quantum phase transitions in two-dimensional XY spin system