Hilbert-space fragmentation selects channels of strong-to-weak spontaneous symmetry breaking

arXiv:2609.26453v1 Announce Type: new 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 $t$-$J_z$ 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 R\'enyi-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 $\nu^k(1-\nu)^k/k^2$, 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.

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 $t$-$J_z$ 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 $\nu^k(1-\nu)^k/k^2$, 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.

16 pages, 5 figures. Comments are welcome!

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2609.26453 [quant-ph]

(or arXiv:2609.26453v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.26453 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Hilbert-space fragmentation selects channels of strong-to-weak spontaneous symmetry breaking

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