Wormhole-induced effective coupling in SYK chains

TL;DR

This paper investigates inhomogeneous SYK chains with large N, revealing how wormhole-like effective couplings emerge through a strong-disorder renormalization group process, connecting ground states to holographic dual descriptions involving wormholes.

Contribution

It introduces a unified approach combining SYK model techniques with SDRG to analyze inhomogeneous chains and shows how wormhole-like effective couplings arise in the ground state.

Findings

Effective hopping interactions are induced between neighboring sites via SDRG decimation.

Ground states can be described by a sequence of wormholes in a discrete holographic framework.

The resulting ground state is factorized with a spacetime structure involving wormholes.

Abstract

Inhomogeneous quantum chains have recently been considered in the context of developing novel discrete realizations of holographic dualities. To advance this programme, we explore the ground states of infinite chains with large number $N$ of Majorana fermions on each site, which interact via on-site $q$-body Sachdev-Ye-Kitaev (SYK) couplings, as well as via additional inhomogeneous hopping terms between nearest-neighbour sites. The hopping parameters are either aperiodically or randomly distributed. Our approach unifies techniques to solve SYK-like models in the large $N$ limit with a real-space renormalization group method known as strong-disorder renormalization group (SDRG). We show that the SDRG decimation of SYK dots linked by a strong hopping induces an effective hopping interaction between their neighbouring sites. If two decimated sites are nearest neighbours, in the large $q$ limit their local ground states admit a holographic dual description in terms of eternal traversable wormholes. At the end of the SDRG procedure, we obtain a factorised ground state of the infinite inhomogeneous SYK chains that we consider, which has a spacetime description involving a sequence of wormholes. This amounts to a local near-boundary description of the bulk geometry in the context of discrete holography.