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arXiv · 2603.10691

Probing the ergodicity breaking transition via violations of random matrix theoretic predictions for local observables

Venelin P. Pavlov·Peter A. Ivanov·Diego Porras·Charlie Nation
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Abstract

Quantum many-body systems can exhibit distinct regimes where dynamics is either ergodic, dynamically exploring an extensive region of available state-space, or non-ergodic, where the dynamics may be restricted. An example is the many-body localization (MBL) transition, where disorder induces non-ergodic behaviour. Most measures of ergodicity notably rely on global quantities, such as level spacing statistics. We explore the ability for a subsystem to probe the ergodicity of dynamics via measurement of local observables, and use expected results from random matrix theory (RMT) as a benchmark for the ergodic regime. We exploit two predictions from RMT as ergodicity is broken: the time evolution of the quantum Fisher information, and a fluctuation-dissipation relation. These are investigated in three different ergodicity breaking mechanisms, namely, as a consequence of transition to integrability, MBL, and Quantum Many-Body Scars (QMBS). We show that the predicted behaviour from RMT can be used as a potential witness for transition to non-ergodic behaviour from the measurement of local observables alone.

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Venelin P. Pavlov, Peter A. Ivanov, Diego Porras, Charlie Nation. 2026-03-11. Probing the ergodicity breaking transition via violations of random matrix theoretic predictions for local observables. https://arxiv.org/abs/2603.10691

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