Universal role of quantum uncertainty in Anderson metal-insulator transition

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• 作者：W.W. Cheng^a ; ^b ; ^{wwcheng@njupt.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Z.J. Zhang^a ; L.Y. Gong^a ; ^c ; S.M. Zhao^a
• 关键词：Quantum uncertainty ; Wigner&ndash ; Yanase skew information ; Anderson metal&ndash ; insulator transition
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：370
• 期：Complete
• 页码：67-76
• 全文大小：930 K

文摘

We explore quantum uncertainty, based on Wigner–Yanase skew information, in various one-dimensional single-electron wave functions. For the power-law function and eigenfunctions in the Aubry–André model, the electronic localization properties are well-defined. For them, we find that quantum uncertainty is relatively small and large for delocalized and localized states, respectively. And around the transition points, the first-order derivative of the quantum uncertainty exhibits singular behavior. All these characters can be used as signatures of the transition from a delocalized phase to a localized one. With this criterion, we also study the quantum uncertainty in one-dimensional disorder system with long-range correlated potential. The results show that the first-order derivative of spectrum-averaged quantum uncertainty is minimal at a certain correlation exponent b=MathURL&_method=retrieve&_eid=1-s2.0-S0003491616300069&_mathId=si46.gif&_user=111111111&_pii=S0003491616300069&_rdoc=1&_issn=00034916&md5=4793eb0e1b0b48d7c8b1d6bd8933264b" title="Click to view the MathML source">αb>mb> for a finite system, and has perfect finite-size scaling behaviors around b=MathURL&_method=retrieve&_eid=1-s2.0-S0003491616300069&_mathId=si46.gif&_user=111111111&_pii=S0003491616300069&_rdoc=1&_issn=00034916&md5=4793eb0e1b0b48d7c8b1d6bd8933264b" title="Click to view the MathML source">αb>mb>. By extrapolating b=MathURL&_method=retrieve&_eid=1-s2.0-S0003491616300069&_mathId=si46.gif&_user=111111111&_pii=S0003491616300069&_rdoc=1&_issn=00034916&md5=4793eb0e1b0b48d7c8b1d6bd8933264b" title="Click to view the MathML source">αb>mb>, the threshold value b=MathURL&_method=retrieve&_eid=1-s2.0-S0003491616300069&_mathId=si58.gif&_user=111111111&_pii=S0003491616300069&_rdoc=1&_issn=00034916&md5=d114129a22dc0fb54767b42cf76cab88" title="Click to view the MathML source">αb>cb>≃1.56±0.02 is obtained for the infinite system. Thus we give another perspective and propose a consistent interpretation for the discrepancies about localization property in the long-range correlated potential model. These results suggest that the quantum uncertainty can provide us with a new physical intuition to the localization transition in these models.