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SUMMARY:Undecidability of the spectral gap in rotationally symmetric Hamil
 tonians - Laura Castilla\, Universidad Complutense de Madrid
DTSTART:20250313T141500Z
DTEND:20250313T151500Z
UID:TALK229246@talks.cam.ac.uk
CONTACT:Subhayan Roy Moulik
DESCRIPTION:The problem of determining the existence of a spectral gap in 
 a lattice quantum spin system was previously shown to be undecidable for o
 ne or more dimensions. In these works\, families of nearest-neighbour inte
 ractions are constructed whose spectral gap depends on the outcome of a Tu
 ring machine Halting problem\, therefore making it impossible for an algor
 ithm to predict its existence.\n\nWhile these models are translationally i
 nvariant\, they are not invariant under the other symmetries of the lattic
 e\, a property which is commonly found in physically relevant cases\, posi
 ng the question of whether the spectral gap is still an undecidable proble
 m for Hamiltonians with stronger symmetry constraints. We give a positive 
 answer to this question\, in the case of models with 4-body (plaquette) in
 teractions on the square lattice satisfying rotation\, but not reflection\
 , symmetry: rotational symmetry is not enough to make the problem decidabl
 e.
LOCATION:MR2
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