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arXiv:2507.11276

Diagnosing phase transitions through time-scale entanglement

Stefan Rohshap, Hirone Ishida, Frederic Bippus, Verhoff, Leonard M., Anna Kauch, Karsten Held, Hiroshi Shinaoka, Markus Wallerberger

Published Jul 15, 2025• 1 citation
arXivHTMLPDF

Abstract

Spatial entanglement of quantum states has become a central paradigm of many-body physics. Here, we unearth a fundamentally different form of entanglement, the entanglement between imaginary time scales. This time-scale entanglement is accessible through quantics tensor train diagnostics (QTTD), where the bond dimension of an $n$-particle correlator encodes the coupling between temporal scales. Our central result is that time-scale entanglement is generically enhanced in the vicinity of phase transitions and crossovers. At quantum critical points, it becomes scale-invariant. We demonstrate time-scale entanglement across a range of systems, including finite-size Hubbard rings, the transverse-field Ising model, the single-impurity Anderson model, and the Mott transition in the Hubbard model. Remarkably, the enhanced time-scale entanglement is largely independent of the specific observable, establishing QTTD as a universal and unbiased diagnostic of criticality.

DOI
10.48550/arxiv.2507.11276

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