Orateur
Description
The system of N fermions, interacting randomly, q at a time is called the SYK dot. These dots are put on a 1D chain and allow for q body interactions between nearest neighbor sites. At large N, this model is known to have two channels of energy transport at very low temperatures: a diffusive (Drude like) mode and a set of critical gapped modes. While these models are not analytically tractable in general, interestingly they show non-fermi liquid behavior at low temperatures. To better understand this behavior, we study the energy retarded Green’s function in the large q limit, where the model becomes analytically solvable. By analyzing the poles, we study the two transport channels and the interactions between them by a phenomenon called ‘pole collisions’, where the dispersion relations display branch point singularities. At zero temperature, the critical poles coalesce into a logarithmic branch cut. Despite this, a gapless, non-hydrodynamic mode survives and continues to dominate energy transport. Our results clarify how energy transport changes across scales in strongly interacting quantum systems and agree with coresponding predictions from holographic theories inspired from string theory.
