Thermal entanglement transitions from strong SU(2) symmetry
Abstract
We study mixed-state entanglement in Gibbs states with strong SU(2) symmetry, focusing on locally interacting spin systems with ferromagnetic interactions. Our main result is to show that finite-temperature ordering transitions are associated with entanglement transitions, and therefore the steady state of strongly symmetric Lindbladians can exhibit entanglement transitions. While in the paramagnetic phase it is known that the distillable entanglement and logarithmic entanglement negativity between two halves of a large system grow logarithmically with the square root of the number of spins, we show that in ferromagnetic phases these quantities grow parametrically faster with system size. To arrive at this result we first establish relations between these mixed-state entanglement measures and spin correlations in states that are singlets under global SU(2) symmetry transformations. We then introduce a semiclassical theory for SU(2) singlet thermal states. While the global singlet constraint generally enters this theory as a complicated function of the full semiclassical spin configuration, we show that in large S limit it simplifies drastically to a Gaussian suppression of total magnetization in disordered phases as well as in ordered phases in the vicinity of continuous thermal phase transitions. This leads us to a field theory describing spin correlations in the singlet sector. Using this we determine the behavior of various probes of mixed-state entanglement at low and at high temperatures, supporting our analytical results using numerical Monte Carlo simulations of a three-dimensional lattice realization of our semiclassical theory. We also use exact numerics in one-dimensional spin-1/2 systems to confirm our predictions for the scaling of mixed-state entanglement with correlation length and system size in the paramagnetic phase.
Related
- Strong-to-Weak Spontaneous Symmetry Breaking Transitions on a Quantum Processor
- Predicting Entanglement Spectra of Gapless Symmetry-Protected Topological States in One Dimension
- Ground-state entanglement and preserved dynamical symmetry in the interacting boson model
- Fractionalization-Induced Time-Reversal Symmetry Breaking at Continuous Superconducting Transitions in Low-Symmetry Kondo Lattices
- Finite-size scaling theory of Rényi thermal entropy for second-order, first-order, and weakly first-order quantum phase transitions
BibTeX
@misc{mo2026thermal,
title = {{Thermal entanglement transitions from strong $\textrmSU(2)$ symmetry}},
author = {Siqi Mo and Ehud Altman and Samuel J. Garratt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00826},
eprint = {2610.00826},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00826},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Thermal entanglement transitions from strong SU(2) symmetry
AU - Siqi Mo
AU - Ehud Altman
AU - Samuel J. Garratt
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00826
UR - https://arxiv.org/abs/2610.00826
AB - We study mixed-state entanglement in Gibbs states with strong SU(2) symmetry, focusing on locally interacting spin systems with ferromagnetic interactions. Our main result is to show that finite-temperature ordering transitions are associated with entanglement transitions, and therefore the steady state of strongly symmetric Lindbladians can exhibit entanglement transitions. While in the paramagnetic phase it is known that the distillable entanglement and logarithmic entanglement negativity between two halves of a large system grow logarithmically with the square root of the number of spins, we show that in ferromagnetic phases these quantities grow parametrically faster with system size. To arrive at this result we first establish relations between these mixed-state entanglement measures and spin correlations in states that are singlets under global SU(2) symmetry transformations. We then introduce a semiclassical theory for SU(2) singlet thermal states. While the global singlet constraint generally enters this theory as a complicated function of the full semiclassical spin configuration, we show that in large S limit it simplifies drastically to a Gaussian suppression of total magnetization in disordered phases as well as in ordered phases in the vicinity of continuous thermal phase transitions. This leads us to a field theory describing spin correlations in the singlet sector. Using this we determine the behavior of various probes of mixed-state entanglement at low and at high temperatures, supporting our analytical results using numerical Monte Carlo simulations of a three-dimensional lattice realization of our semiclassical theory. We also use exact numerics in one-dimensional spin-1/2 systems to confirm our predictions for the scaling of mixed-state entanglement with correlation length and system size in the paramagnetic phase.
ER -