Hilbert-space fragmentation selects channels of strong-to-weak spontaneous symmetry breaking
Abstract
Strong-to-weak spontaneous symmetry breaking (SWSSB) can occur in a maximally mixed charge sector even when ordinary charged correlations vanish. We study this order when a charge sector splits into dynamically disconnected fragments. In a one-dimensional t-Jz chain with species-resolved dephasing, each fragment is labeled by a conserved spin word. A charged transfer between separated finite intervals preserves that word only if the intervening spins satisfy a periodicity constraint. In the full-state two-point sense, we use this constraint to prove the absence of long-range fidelity and Rényi-1 order in typical fixed-composition fragments, uniformly over all norm-bounded charged operators in any prescribed finite interval. A fragment with primitive spin-word period k supports a k-particle channel with exact long-distance value νk(1−ν)k/k2, and no charged operator on fewer than k sites can carry this order. A transverse exchange connects the fragments while preserving the global charges and restores the full-sector steady state at finite size. The conserved spin word therefore selects the local channels that can support mixed-state order.
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BibTeX
@misc{xu2026hilbertspace,
title = {{Hilbert-space fragmentation selects channels of strong-to-weak spontaneous symmetry breaking}},
author = {Mingdi Xu and Kaixiang Lu and Daoguang Li and Lei Pan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26453},
eprint = {2609.26453},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26453},
}
RIS
TY - UNPB
TI - Hilbert-space fragmentation selects channels of strong-to-weak spontaneous symmetry breaking
AU - Mingdi Xu
AU - Kaixiang Lu
AU - Daoguang Li
AU - Lei Pan
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26453
UR - https://arxiv.org/abs/2609.26453
AB - Strong-to-weak spontaneous symmetry breaking (SWSSB) can occur in a maximally mixed charge sector even when ordinary charged correlations vanish. We study this order when a charge sector splits into dynamically disconnected fragments. In a one-dimensional t-J_z chain with species-resolved dephasing, each fragment is labeled by a conserved spin word. A charged transfer between separated finite intervals preserves that word only if the intervening spins satisfy a periodicity constraint. In the full-state two-point sense, we use this constraint to prove the absence of long-range fidelity and Rényi-1 order in typical fixed-composition fragments, uniformly over all norm-bounded charged operators in any prescribed finite interval. A fragment with primitive spin-word period k supports a k-particle channel with exact long-distance value ν^k(1−ν)^k/k^2, and no charged operator on fewer than k sites can carry this order. A transverse exchange connects the fragments while preserving the global charges and restores the full-sector steady state at finite size. The conserved spin word therefore selects the local channels that can support mixed-state order.
ER -