Critical Touching of Temporal Entanglement Transitions
Abstract
Equilibrium phase transitions are conventionally categorized into first-order and continuous phase transitions. Far from equilibrium, many new transitions emerge during the real-time evolution of quantum systems. One such transition is the temporal entanglement transition (TET) characterized by the nonanalyticity of the entanglement spectrum. So far, all TETs occur through a linear crossing of the leading Schmidt levels in different symmetry sectors, resembling a first-order transition in equilibrium. A natural question is whether a continuous TET, featured by entanglement spectrum touching, is possible. In a periodically driven transverse J1-J2 Ising chain, we show that two such TETs can merge into a critical touching, where the leading levels meet tangentially without exchanging, realizing the temporal analog of a continuous phase transition. Near the critical frequency, the temporal separation of the two TETs vanishes continuously and its derivative with respect to frequency diverges, a nonanalytic signature that is absent in a single first-order TET. This finite-frequency touching arises from the interplay between a weak symmetry-preserving perturbation of the product initial state and Floquet corrections. Further extending the frequency scan reveals a second critical touching at a higher frequency, and the two critical frequencies enclose a finite window with no TET. These features can be understood from a second-order Floquet Hamiltonian and persist across a broad range of coupling ratios, establishing the critical touching as a distinct form of TET.
Related
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BibTeX
@misc{wang2026critical,
title = {{Critical Touching of Temporal Entanglement Transitions}},
author = {Ting-Long Wang and Shi-Xin Zhang and Shuai Yin and Yi-Fan Jiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23513},
eprint = {2609.23513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23513},
}
RIS
TY - UNPB
TI - Critical Touching of Temporal Entanglement Transitions
AU - Ting-Long Wang
AU - Shi-Xin Zhang
AU - Shuai Yin
AU - Yi-Fan Jiang
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23513
UR - https://arxiv.org/abs/2609.23513
AB - Equilibrium phase transitions are conventionally categorized into first-order and continuous phase transitions. Far from equilibrium, many new transitions emerge during the real-time evolution of quantum systems. One such transition is the temporal entanglement transition (TET) characterized by the nonanalyticity of the entanglement spectrum. So far, all TETs occur through a linear crossing of the leading Schmidt levels in different symmetry sectors, resembling a first-order transition in equilibrium. A natural question is whether a continuous TET, featured by entanglement spectrum touching, is possible. In a periodically driven transverse J_1-J_2 Ising chain, we show that two such TETs can merge into a critical touching, where the leading levels meet tangentially without exchanging, realizing the temporal analog of a continuous phase transition. Near the critical frequency, the temporal separation of the two TETs vanishes continuously and its derivative with respect to frequency diverges, a nonanalytic signature that is absent in a single first-order TET. This finite-frequency touching arises from the interplay between a weak symmetry-preserving perturbation of the product initial state and Floquet corrections. Further extending the frequency scan reveals a second critical touching at a higher frequency, and the two critical frequencies enclose a finite window with no TET. These features can be understood from a second-order Floquet Hamiltonian and persist across a broad range of coupling ratios, establishing the critical touching as a distinct form of TET.
ER -