Discrete time liquids
Abstract
Discrete time crystals exhibit robust subharmonic oscillations, spontaneously breaking the discrete time-translation symmetry of a periodic drive. Since their emergence, the question of whether other types of temporal many-body order can exist has attracted considerable attention. Here we identify discrete time liquids -- a new form of spatiotemporal order characterized by short-range temporal coherence as a result of time-solitons. We study a two-dimensional spin system coupled to a finite-temperature cavity, whose fluctuations provide a noisy, approximately periodic drive with only finite temporal coherence. Remarkably, the spins nevertheless form a metastable state with robust period-doubled dynamics over an extended parameter regime. Unlike a time crystal, this state has only finite temporal coherence: individual trajectories stochastically switch between the two symmetry-related temporal configurations of the period-doubled response. We identify these switches as time-solitons: topological defects in temporal order that preserve local period doubling while destroying long-range temporal coherence, thereby producing the time liquid state. We propose a minimal model which reproduces the distribution of temporal correlations of the many-body system, suggesting a general description of the time liquid as a time crystal with a finite density of time-solitons. Because these solitons can occur at arbitrary times, ensemble averaging restores continuous time-translation symmetry, raising the intriguing possibility that discrete time liquids can exist in thermal equilibrium.
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BibTeX
@misc{wang2026discrete,
title = {{Discrete time liquids}},
author = {Zuo Wang and Paul M. Schindler and Marin Bukov and Marios H. Michael},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30266},
eprint = {2610.30266},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30266},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Discrete time liquids
AU - Zuo Wang
AU - Paul M. Schindler
AU - Marin Bukov
AU - Marios H. Michael
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30266
UR - https://arxiv.org/abs/2610.30266
AB - Discrete time crystals exhibit robust subharmonic oscillations, spontaneously breaking the discrete time-translation symmetry of a periodic drive. Since their emergence, the question of whether other types of temporal many-body order can exist has attracted considerable attention. Here we identify discrete time liquids -- a new form of spatiotemporal order characterized by short-range temporal coherence as a result of time-solitons. We study a two-dimensional spin system coupled to a finite-temperature cavity, whose fluctuations provide a noisy, approximately periodic drive with only finite temporal coherence. Remarkably, the spins nevertheless form a metastable state with robust period-doubled dynamics over an extended parameter regime. Unlike a time crystal, this state has only finite temporal coherence: individual trajectories stochastically switch between the two symmetry-related temporal configurations of the period-doubled response. We identify these switches as time-solitons: topological defects in temporal order that preserve local period doubling while destroying long-range temporal coherence, thereby producing the time liquid state. We propose a minimal model which reproduces the distribution of temporal correlations of the many-body system, suggesting a general description of the time liquid as a time crystal with a finite density of time-solitons. Because these solitons can occur at arbitrary times, ensemble averaging restores continuous time-translation symmetry, raising the intriguing possibility that discrete time liquids can exist in thermal equilibrium.
ER -