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SUMMARY:Haldane relation for interacting dimers - Alessandro Giuliani (Rom
 e 3)
DTSTART:20171010T151500Z
DTEND:20171010T161500Z
UID:TALK82321@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:In this talk I will review some recent results on the existenc
 e and nature\nof the scaling limit of interacting\, close-packed\, dimers 
 on the\ntwo-dimensional square lattice. By constructive Renormalization Gr
 oup\ntechniques\, we compute: the multipoint dimer correlations\, which di
 splay\nnon-trivial critical exponents\, continuously varying with the inte
 raction\nstrength\; and the height fluctuations\, which\, after proper coa
 rse graining\nand rescaling\, converge to the massless Gaussian field with
  a suitable\ninteraction-dependent pre-factor (`amplitude'). We also prove
  the identity\nbetween the critical exponent of the two-point dimer correl
 ation and the\namplitude of this massless Gaussian field. This identity is
  the\nrestatement\, in the context of interacting dimers\, of one of the H
 aldane\nuniversality relations\, part of his Luttinger liquid conjecture\,
 \noriginally formulated in the context of one-dimensional interacting Ferm
 i\nsystems. Its  proof requires the combined use of an exact lattice Ward\
 nIdentity for the lattice theory\, with the chiral Ward Identites of a\nco
 ntinuum reference model\, which describes the infrared fixed point of the\
 ninteracting theory.\nJoint work with V. Mastropietro and F. Toninelli.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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