Giuseppe Di Giulio, Inhomogeneous SYK chains, renormalization group and wormholes

Wednesday 26 Feb 2025, 11:15 → 12:30 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

Abstract: Motivated by exploring the reach of the holographic principle in discrete hyperbolic spaces, we study a chain of Sachdev-Ye-Kitaev (SYK) clusters coupled by inhomogeneous hopping terms. The couplings are distributed according to an aperiodic sequence deterministically generated that does not display periodic patterns at any scale. In the limit of infinitely many onsite degrees of freedom, the SYK chain is described by coupled Schwinger-Dyson (SD) equations. To access the ground state of this model, we adopt a perturbative real-space renormalization group procedure for systems described by SD equations. The ground state of the chain turns out to be factorized into states coupling two sites, whose spatial distribution reflects the aperiodic modulation of the hoppings in the original chain. We finally provide a geometric description of the ground state in terms of eternal traversable wormholes.