We show that, after ensemble averaging, the low temperature phase of a conjugate pair of uncoupled, quantum chaotic, non-Hermitian systems such as the Sachdev-Ye-Kitaev (SYK) model or the Ginibre ensemble of random matrices is dominated by saddle points that couple replicas and conjugate replicas. This results in a nearly flat free energy that terminates in a first-order phase transition. In the case of the SYK model, we show explicitly that the spectrum of the effective replica theory has a gap. These features are strikingly similar to those induced by wormholes in the gravity path integral which suggests a close relation between both configurations. For a nonchaotic SYK, the results are qualitatively different: the spectrum is gapless in the low temperature phase and there is an infinite number of second order phase transitions unrelated to the restoration of replica symmetry.

• Received 7 May 2021
• Revised 12 September 2021
• Accepted 28 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.081601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society