PreprintCC BY 4.0arXiv
Lieb-Robinson bounds for irreversible dynamics via adaptive Dyson expansion
Abstract
In this note, we study a broad class of time-dependent and irreversible dynamics for quantum spin systems in both finite and infinite volume. We develop a simple and flexible strategy for expanding commutators of the form [A,τs,t B] in terms of self-avoiding paths of sets, where A and B are local operators and τs,t is the Heisenberg time evolution. This adaptive Dyson expansion requires no backwards time evolution and is thus also applicable to irreversible dynamics. Furthermore, we discuss how such an expansion directly implies Lieb-Robinson bounds. A central feature of our result is that the obtained Lieb-Robinson bounds are independent of any Hamiltonian and dissipative on-site terms of the generator.
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BibTeX
@misc{rubiliani2026liebrobinson,
title = {{Lieb-Robinson bounds for irreversible dynamics via adaptive Dyson expansion}},
author = {Carla Rubiliani and Marius Wesle and Tom Wessel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12731},
eprint = {2610.12731},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12731},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lieb-Robinson bounds for irreversible dynamics via adaptive Dyson expansion
AU - Carla Rubiliani
AU - Marius Wesle
AU - Tom Wessel
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12731
UR - https://arxiv.org/abs/2610.12731
AB - In this note, we study a broad class of time-dependent and irreversible dynamics for quantum spin systems in both finite and infinite volume. We develop a simple and flexible strategy for expanding commutators of the form [A,τ_s,t B] in terms of self-avoiding paths of sets, where A and B are local operators and τ_s,t is the Heisenberg time evolution. This adaptive Dyson expansion requires no backwards time evolution and is thus also applicable to irreversible dynamics. Furthermore, we discuss how such an expansion directly implies Lieb-Robinson bounds. A central feature of our result is that the obtained Lieb-Robinson bounds are independent of any Hamiltonian and dissipative on-site terms of the generator.
ER -