Diagnosing phase transitions through time-scale entanglement
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 -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.
Cite
@article{arxiv.2507.11276,
title = {Diagnosing phase transitions through time-scale entanglement},
author = {Stefan Rohshap and Hirone Ishida and Frederic Bippus and Leonard M. Verhoff and Anna Kauch and Karsten Held and Hiroshi Shinaoka and Markus Wallerberger},
journal= {arXiv preprint arXiv:2507.11276},
year = {2026}
}