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The partition function zeroes of quantum critical points

Crompton, P.R. (2009) The partition function zeroes of quantum critical points. Nuclear Physics B, 810 (3). pp. 542-562. ISSN 0550-3213

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Abstract

The Lee–Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity ehΔτ, and the Euclidean-time lattice spacing Δτ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as Parity. We now present a first numerical analysis for this new zeroes approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009 Elsevier B.V. This is an author produced version of a paper published in Nuclear Physics B. Uploaded in accordance with the publisher's self-archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 21 May 2009 09:18
Last Modified: 08 Feb 2013 17:06
Published Version: http://dx.doi.org/10.1016/j.nuclphysb.2008.10.011
Status: Published
Publisher: Elsevier B.V.
Refereed: Yes
Identification Number: 10.1016/j.nuclphysb.2008.10.011
URI: http://eprints.whiterose.ac.uk/id/eprint/8626

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