Fixed Points, Floquet Entanglement Asymmetry, and Quantum Mpemba Effects
Abstract
We investigate the dynamics of entanglement asymmetry in periodically driven two-dimensional conformal field theories with a global U(1) symmetry, using a dynamical-system description based on iterated conformal maps, in particular Möbius maps. Starting from a symmetry-breaking excited state prepared by a local operator insertion, we show that a broad range of nonequilibrium phenomena, including local symmetry restoration, the quantum Mpemba effect, and its inverse, admit a simple geometric description in terms of the invariant data of the conformal map. We explicitly demonstrate this using Möbius maps, for which the invariant structure is described by the conjugacy classes. In particular, the dynamics of entanglement asymmetry is determined by the relative positions of the state-preparing operator insertion, the subsystem, and the fixed points, yielding distinct patterns of growth, decay, oscillation, and saturation. We further argue that this geometric picture extends to general holomorphic maps, establishing the conformal-map dynamics as a natural framework for organizing the phenomenology of entanglement asymmetry in periodically driven two-dimensional conformal field theories.
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BibTeX
@misc{das2026fixed,
title = {{Fixed Points, Floquet Entanglement Asymmetry, and Quantum Mpemba Effects}},
author = {Jayashish Das and Filiberto Ares and Arnab Kundu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17724},
eprint = {2609.17724},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17724},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fixed Points, Floquet Entanglement Asymmetry, and Quantum Mpemba Effects
AU - Jayashish Das
AU - Filiberto Ares
AU - Arnab Kundu
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17724
UR - https://arxiv.org/abs/2609.17724
AB - We investigate the dynamics of entanglement asymmetry in periodically driven two-dimensional conformal field theories with a global U(1) symmetry, using a dynamical-system description based on iterated conformal maps, in particular Möbius maps. Starting from a symmetry-breaking excited state prepared by a local operator insertion, we show that a broad range of nonequilibrium phenomena, including local symmetry restoration, the quantum Mpemba effect, and its inverse, admit a simple geometric description in terms of the invariant data of the conformal map. We explicitly demonstrate this using Möbius maps, for which the invariant structure is described by the conjugacy classes. In particular, the dynamics of entanglement asymmetry is determined by the relative positions of the state-preparing operator insertion, the subsystem, and the fixed points, yielding distinct patterns of growth, decay, oscillation, and saturation. We further argue that this geometric picture extends to general holomorphic maps, establishing the conformal-map dynamics as a natural framework for organizing the phenomenology of entanglement asymmetry in periodically driven two-dimensional conformal field theories.
ER -