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Emptiness Formation Probability

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, The Technion, Haifa, Israel

    Nicholas Crawford

  2. Department of Mathematics, University of Rochester, Rochester, NY, USA

    Stephen Ng

  3. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, USA

    Shannon Starr

Authors
  1. Nicholas Crawford
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  2. Stephen Ng
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  3. Shannon Starr
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Correspondence to Shannon Starr.

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Communicated by R. Seiringer

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Crawford, N., Ng, S. & Starr, S. Emptiness Formation Probability. Commun. Math. Phys. 345, 881–922 (2016). https://doi.org/10.1007/s00220-016-2689-5

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  • DOI: https://doi.org/10.1007/s00220-016-2689-5

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