Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits

Gabriel O. Alves; Felix Fritzsch; Pieter W. Claeys

doi:10.22331/q-2025-12-15-1949

Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits

Gabriel O. Alves, Felix Fritzsch, and Pieter W. Claeys

Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

Published:	2025-12-15, volume 9, page 1949
Editor:	Mark Mitchison
Eprint:	arXiv:2504.08517v2
Doi:	https://doi.org/10.22331/q-2025-12-15-1949
Citation:	Quantum 9, 1949 (2025).

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Abstract

The eigenstate thermalization hypothesis (ETH) is the leading interpretation in our current understanding of quantum thermalization. Recent results uncovered strong connections between quantum correlations in thermalizing systems and the structure of free probability theory, leading to the notion of full ETH. However, most studies have been performed for ergodic systems and it is still unclear whether or how full ETH manifests in ergodicity-breaking models. We fill this gap by studying standard probes of full ETH in ergodicity-breaking quantum circuits, presenting numerical and analytical results for interacting integrable systems. These probes can display distinct behavior and undergo a different scaling than the ones observed in ergodic systems. For the analytical results we consider an interacting integrable dual-unitary model and present the exact eigenstates, allowing us to analytically express common probes for full ETH. We discuss the underlying mechanisms responsible for these differences and show how the presence of solitons dictates the behavior of ETH-related quantities in the dual-unitary model. We show numerical evidence that this behavior is sufficiently generic away from dual-unitarity when restricted to the appropriate symmetry sectors.

Featured image: According to the eigenstate thermalization hypothesis (ETH), eigenstates of quantum many-body systems appear thermal whenever local observables are probed. For such ergodic systems, the dynamics of out-of-time order correlators can be decomposed in the sum of thermal cumulants — an ETH-based analogue of free cumulants. This decomposition is based on the combinatorics of non-crossing partitions and correctly captures the long-time behavior of OTOCs. In this work, we investigate the behavior of such probes and their underlying structure in ergodicity-breaking quantum circuits.

► BibTeX data

@article{Alves2025probesoffull,
  doi = {10.22331/q-2025-12-15-1949},
  url = {https://doi.org/10.22331/q-2025-12-15-1949},
  title = {Probes of {F}ull {E}igenstate {T}hermalization in {E}rgodicity-{B}reaking {Q}uantum {C}ircuits},
  author = {Alves, Gabriel O. and Fritzsch, Felix and Claeys, Pieter W.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1949},
  month = dec,
  year = {2025}
}

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