Emptiness Formation Probability

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• 作者：Nicholas Crawford ; Stephen Ng ; Shannon Starr
• 刊名：Communications in Mathematical Physics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：345
• 期：3
• 页码：881-922
• 全文大小：1,102 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Quantum Physics
  Quantum Computing, Information and Physics
  Complexity
  Statistical Physics
  Relativity and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0916
• 卷排序：345

文摘

We present rigorous upper and lower bounds on the emptiness formation probability for the ground state of a spin-1/2 Heisenberg XXZ quantum spin system. For a d-dimensional system we find a rate of decay of the order \({\exp(-c L^{d+1})}\) where L is the sidelength of the box in which we ask for the emptiness formation event to occur. In the \({d=1}\) case this confirms previous predictions made in the integrable systems community, though our bounds do not achieve the precision predicted by Bethe ansatz calculations. On the other hand, our bounds in the case \({d \geq 2}\) are new. The main tools we use are reflection positivity and a rigorous path integral expansion, which is a variation on those previously introduced by Toth, Aizenman-Nachtergaele and Ueltschi.Communicated by R. Seiringer