Andrea Legramandi - Universitá di Trento

Complexity and Chaos in Quantum Many-Body Systems

Quantum systems composed of many interacting particles are intrinsically difficult to model. When a quantum many-body system is subject to disorder, it can undergo transitions to non-ergodic and localized regimes, which can significantly reduce the number of relevant basis states. It remains an open question whether such transitions are also directly related to an abrupt change in the system's complexity.

In this talk, I will study the transition from chaotic to integrable phases in the paradigmatic Rosenzweig—Porter and SYK models, comparing complementary complexity markers, such as fractal dimension, von Neumann entropy, and stabilizer Rényi entropy.

For all three markers, finite-size scaling reveals sharp transitions between high- and low-complexity regimes, which, however, can occur at different critical points. As a consequence, while in the ergodic and localized regimes the markers align, they diverge significantly in the presence of an intermediate fractal phase.

As our results show, different markers capture complementary facets of complexity, making it necessary to combine them to obtain a comprehensive diagnosis of phase transitions.

The divergence between different complexity markers also has significant consequences for the classical simulability of chaotic many-body systems.