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Extension of the SYK model to 1+1 dimensions in the strong coupling limit

Vidal Yunge, A. A., De Martino, A. ORCID: 0000-0002-3656-0419 & Tagliacozzo, A. (2023). Extension of the SYK model to 1+1 dimensions in the strong coupling limit. Physical Review B, 108(7), article number 075428. doi: 10.1103/physrevb.108.075428


We study a 1+1 (space-time)-dimensional extension of the 0+1-dimensional Sachdev-Ye-Kitaev model for N Majorana fermions, with random all-to-all quartic interactions, averaged over disorder. At large interaction couplings and large N, the conformal symmetry of the effective action emerges, which is not broken spontaneously as in the original 0+1 SYK model. Two-point correlators are obtained from a coupling expansion of the Schwinger-Dyson equations. For N=4, the model can be mapped onto complex fermions and solved exactly via the bosonization technique, featuring two branches of excitations: a gapped "pseudocharge"mode and a gapless "pseudospin"mode. We give an approximate analytic form of the two-point correlators at large distances and zero temperature for N=4, which is adopted heuristically to evaluate an approximation to the large-N free energy in the zero temperature limit, numerically. The fact that this energy displays an absolute minimum at a finite value of the gap, though in a restricted range of parameters, suggests that a gapped branch of excitations is also present in our extension of the model at least in that range of parameters.

Publication Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
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