Traversable wormhole in coupled SYK models with imbalanced interactions

TL;DR

This paper investigates the stability of the wormhole dual in coupled SYK models under imbalanced interactions, showing that key wormhole features persist in certain imbalanced regimes and proposing experimental realizations.

Contribution

It demonstrates that the wormhole ground state remains stable under interaction imbalance and explores the maximally imbalanced limit with potential for laboratory implementation.

Findings

Wormhole signatures persist despite interaction imbalance.

Maximally imbalanced limit retains some wormhole features.

Potential experimental setups for realizing imbalanced SYK models.

Abstract

A pair of identical Sachdev-Ye-Kitaev (SYK) models with bilinear coupling forms a quantum dual of a traversable wormhole, with a ground state close to the so called thermofield double state. We use adiabaticity arguments and numerical simulations to show that the character of the ground state remains unchanged when interaction strengths in the two SYK models become imbalanced. Analysis of thermodynamic and dynamical quantities highlights the key signatures of the wormhole phase in the imbalanced case. Further adiabatic evolution naturally leads to the 'maximally imbalanced' limit where fermions in a single SYK model are each coupled to a free Majorana zero mode. This limit is interesting because it could be more easily realized using various setups proposed to implement the SYK model in a laboratory. We find that this limiting case is marginal in that it retains some of the characteristic signatures of the wormhole physics, such as the spectral gap and revival dynamics, but lacks others so that it likely does not represent the full-fledged wormhole dual. We discuss how this scenario could be implemented in the proposed realization of the SYK physics in quantum wires of finite length coupled to a disordered quantum dot.