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arXiv:1609.01835 · Annals of Physics

Quantum phase transition by employing trace distance along with the density matrix renormalization group

Da-Wei Luo, Jing‐Bo Xu

Published Jan 5, 2015• 12 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2014.12.023

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We investigate the quantum phase transitions of spin systems in one and two dimensions by employing trace distance and multipartite entanglement along with the real-space quantum renormalization group method. As illustration examples, a one-dimensional and a two-dimensional XY models are considered. It is shown that the quantum phase transitions of these spin-chain systems can be revealed by the singular behaviors of the first derivatives of renormalized trace distance and multipartite entanglement in the thermodynamics limit. Moreover, we find that the renormalized trace distance and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical points.