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Energy correlations in random transverse field Ising spin chains

Refael, Gil and Fisher, Daniel S. (2004) Energy correlations in random transverse field Ising spin chains. Physical Review B, 70 (6). Art. No. 064409. ISSN 1098-0121. doi:10.1103/PhysRevB.70.064409.

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The end-to-end energy-energy correlations of random transverse field quantum Ising spin chains are computed using a generalization of an asymptotically exact real space renormalization group (RG) previously introduced. Away from the critical point, the average energy-energy correlations decay exponentially with a correlation length that is the same as that of the spin-spin correlations. The typical correlations, however, decay exponentially with a characteristic length, proportional to the square root of the primary correlation length. At the quantum critical point, the average correlations decay subexponentially as [overline C[sub L]]~e–const L1/3, whereas the typical correlations decay faster, as ~e<sup>-Ksqrt(L)</sup>, with K a random variable with a universal distribution. The critical energy-energy correlations behave very similarly to the smallest gap, computed previously; this is explained in terms of the RG flow and the excitation structure of the chain. In order to obtain the energy correlations, an extension of the previously used methods was needed; here, this was carried out via RG transformations that involve a sequence of unitary transformations.

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Additional Information:©2004 The American Physical Society (Received 8 August 2003; revised 28 April 2004; published 17 August 2004) This work has been supported in part by the National Science Foundation via DMR-9976621, DMR-9809363, and the MRSEC at Harvard. One of us (G.R.) was supported in part by a Harvard Merit Fellowship.
Subject Keywords:Ising model; renormalisation
Issue or Number:6
Record Number:CaltechAUTHORS:REFprb04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7130
Deposited By: Archive Administrator
Deposited On:09 Jan 2007
Last Modified:08 Nov 2021 20:39

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