Stabilizer Rényi Entropy Transitions in Coupled Sachdev-Ye-Kitaev Models Reveal First-Order Phase Changes

Entanglement and quantum magic represent distinct resources that underpin complex physical phenomena beyond classical simulation, and understanding both is crucial for advancing quantum technologies. Pengfei Zhang, Shuyan Zhou, and Ning Sun, all from Fudan University, investigate quantum magic using a measure called the stabilizer Rényi entropy, a tool previously limited to relatively small systems. This research establishes a new analytical framework for calculating this entropy in a solvable model, the Sachdev-Ye-Kitaev model, allowing for calculations on much larger scales. The team identifies abrupt transitions in the entropy as temperature changes, revealing a hidden characteristic of the system undetectable through conventional measurements, and opens new avenues for exploring strongly correlated fermionic systems where the entropy itself can act as a key indicator of phase transitions.

Stabilizer Renyi Entropy and SYK Model Analysis

Quantum resources empower quantum systems to perform tasks beyond the reach of classical computers. While quantum entanglement is well-studied, understanding quantum magic, a distinct resource driving quantum computation, remains a significant challenge. This work presents a general framework for analysing the stabilizer Rényi entropy (SRE) in solvable Sachdev-Ye-Kitaev (SYK) models, leveraging the large-N limit to simplify calculations. This approach allows scientists to probe the complex behaviour of these systems and gain insights into the nature of quantum magic. The researchers applied this framework to the Maldacena-Qi coupled SYK model, a system amenable to precise theoretical analysis. They developed a path-integral formalism to calculate the SRE, a quantitative measure of quantum magic. This analysis revealed a series of abrupt transitions as temperature is adjusted, indicating changes in the system’s quantum magical properties and demonstrating the potential for the SRE to reveal hidden structures within strongly interacting fermionic systems.

First-Order Transitions Reveal Quantum Magic Structure

Scientists have achieved a breakthrough in understanding quantum magic by developing a new method for analysing the stabilizer Rényi entropy (SRE) in complex quantum systems. Focusing on the Maldacena-Qi coupled SYK model, they uncovered previously hidden structures within strongly interacting fermionic systems. The team established a path-integral formalism enabling precise calculation of the SRE and discovered a series of first-order transitions as temperature changes. Experiments revealed three distinct first-order transitions in the SRE, indicating abrupt changes in the system’s quantum magical properties. Crucially, one of these transitions is intrinsic to the SRE itself and cannot be detected through conventional thermodynamic measurements. This intrinsic transition arises from a change in the connectivity of different pathways within the path-integral formulation, analogous to the formation of replica wormholes, and demonstrates that the SRE can reveal hidden structures inaccessible through standard equilibrium observables.

Stabilizer Entropy Reveals New Quantum Phases

This research establishes a framework for analysing a measure of quantum complexity, the stabilizer Rényi entropy, within solvable models of quantum systems. By applying this method to a specific coupled model, scientists identified a series of abrupt transitions in the entropy as temperature changes, revealing intrinsic properties not detectable through conventional thermodynamic measurements. These findings demonstrate the potential for the stabilizer Rényi entropy to function as an order parameter, characterizing new phases in strongly correlated fermionic systems. The team’s analysis further reveals how the entropy changes with increasing temperature, pinpointing distinct transitions related to both the system’s internal connectivity and the well-known Hawking-Page transition governing thermal behaviour. They observed that these transitions manifest as qualitative changes in how different replicas of the quantum system connect, indicating a fundamental shift in the system’s structure. While the study focuses on specific models, the authors acknowledge that the observed behaviour may transition into crossovers with larger coupling strengths, and future work could explore the broader applicability of this framework to other complex quantum systems and investigate the precise relationship between the stabilizer Rényi entropy and emergent phases of matter.