Integrability and conformal data of the dimer model

Morin-Duchesne, Alexi, Rasmussen, Jorgen and Ruelle, Philippe (2016) Integrability and conformal data of the dimer model. Journal of Physics A: Mathematical and Theoretical, 49 17: 1-57. doi:10.1088/1751-8113/49/17/174002

Author Morin-Duchesne, Alexi
Rasmussen, Jorgen
Ruelle, Philippe
Title Integrability and conformal data of the dimer model
Journal name Journal of Physics A: Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
Publication date 2016-03-17
Year available 2016
Sub-type Article (original research)
DOI 10.1088/1751-8113/49/17/174002
Open Access Status Not Open Access
Volume 49
Issue 17
Start page 1
End page 57
Total pages 57
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2017
Language eng
Formatted abstract
The central charge of the dimer model on the square lattice is still being debated in the literature. In this paper, we provide evidence supporting the consistency of a c = -2 description. Using Lieb's transfer matrix and its description in terms of the Temperley–Lieb algebra TLn at beta =0, we provide a new solution of the dimer model in terms of the model of critical dense polymers on a tilted lattice and offer an understanding of the lattice integrability of the dimer model. The dimer transfer matrix is analyzed in the scaling limit, and the result for L0 - c/24 is expressed in terms of fermions. Higher Virasoro modes are likewise constructed as limits of elements of TLn and are found to yield a c = -2 realization of the Virasoro algebra, familiar from fermionic bc ghost systems. In this realization, the dimer Fock spaces are shown to decompose, as Virasoro modules, into direct sums of Feigin–Fuchs modules, themselves exhibiting reducible yet indecomposable structures. In the scaling limit, the eigenvalues of the lattice integrals of motion are found to agree exactly with those of the c = -2 conformal integrals of motion. Consistent with the expression for L0 - c/24 obtained from the transfer matrix, we also construct higher Virasoro modes with c = 1 and find that the dimer Fock space is completely reducible under their action. However, the transfer matrix is found not to be a generating function for the c = 1 integrals of motion. Although this indicates that Lieb's transfer matrix description is incompatible with the c = 1 interpretation, it does not rule out the existence of an alternative, c = 1 compatible, transfer matrix description of the dimer model.
Keyword Dimer model
Critical dense polymers
Temperley-Lieb algebra
Conformal field theory
Integrals of motion
Feigin-Fuchs modules
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Thu, 24 Mar 2016, 19:30:41 EST by Jorgen Rasmussen on behalf of Mathematics