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International Journal of Theoretical Physics

Negativity and Quantum Phase Transition in the Spin Model Using the Quantum Renormalization-group Method

Wen‐Yang Sun, Shuai Xu, Cheng‐Cheng Liu, Liu Ye

Published Dec 19, 2015• 9 citations
Publisher
DOI
10.1007/s10773-015-2890-x

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In this paper, we use the negativity and geometric quantum discord (GQD) to investigate the quantum phase transition (QPT) in the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii–Moriya (DM) interaction using the quantum renormalization-group method, and the results show that the negativity and GQD can both obtain the quantum critical points associated with QPTs after several iterations of the renormalization. In addition to this, we discuss how the strength of the DM interaction and anisotropic parameter make the effect on the negativity and GQD for different RG steps. At last, we give out the relationship between negativity and GQD, and verify that with anisotropy parameter and the strength of DM interaction increased, the squared negativity and the normalization of GQD tend to equal in this model.
The global quench dynamics of 3-state quantum Potts spin chain is investigated for different initial states using quantum renormalization group method. The results show that the value of negativity is maximum or minimum at quantum phase transition point and the steady value of negativity is also dependent on the initial states, which means that the dynamic behavior is strongly dependent on the initial states. The range of negativity is decreases as the size of system increases for different steps of renormalization group transformations.