Kirill Shtengel et al 2005 J. Phys. A: Math. Gen. 38 L589 doi:10.1088/0305-4470/38/36/L01
No sliding in time
FREE ARTICLEKirill Shtengel1,2, Chetan Nayak3, Waheb Bishara1 and Claudio Chamon4
Show affiliationsLETTER TO THE EDITOR
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.
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Issue 36 (9 September 2005)
Received 1 July 2005
Published 23 August 2005
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No sliding in time
Kirill Shtengel et al 2005 J. Phys. A: Math. Gen. 38 L589
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