Shtengel, Kirill and Nayak, Chetan and Bishara, Waheb and Chamon, Claudio (2005) No sliding in time. Journal of Physics A: Mathematical and General, 38 (36). L589-L595. ISSN 0305-4470 http://resolver.caltech.edu/CaltechAUTHORS:SHTjpa05
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In this letter, we analyse the following apparent paradox: as has been recently proved by Hastings (2004 Phys. Rev. 69 104431), under a general set of conditions, if a local Hamiltonian has a spectral gap above its (unique) ground state (GS), all connected equal-time correlation functions of local operators decay exponentially with distance. On the other hand, statistical mechanics provides us with examples of 3D models displaying so-called sliding phases (O'Hern et al 1999 Phys. Rev. Lett. 83 2745) which are characterized by the algebraic decay of correlations within 2D layers and exponential decay in the third direction. Interpreting this third direction as time would imply a gap in the corresponding (2+1)D quantum Hamiltonian which would seemingly contradict Hastings' theorem. The resolution of this paradox lies in the non-locality of such a quantum Hamiltonian.
|Additional Information:||Copyright © Institute of Physics and IOP Publishing Limited 2005. Received 1 July 2005. Published 23 August 2005. Print publication: Issue 36 (9 September 2005) The authors are grateful to S Kivelson, S Chakravarty, A Kitaev, I Dimov, X-G Wen, E Fradkin, G Refael and I Klich for useful discussions and comments. KS and CN have been supported by the ARO under grant no. W911NF-04-1-0236. CN has also been supported by the NSF under grant no. DMR-0411800. CC has been supported by the NSF under grant no. DMR-0305482.|
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|Deposited On:||11 Dec 2006|
|Last Modified:||26 Dec 2012 09:21|
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