Mixing-time scaling and classification of nonperiodic word fragments

Determine how the mixing time depends on system size L and transverse exchange J_\perp, and classify the nonlinear-order channels of more general nonperiodic spin words in the fragmented one-dimensional t-J_z chain with species-resolved dephasing.

Background

The paper establishes the finite-size stationary-state endpoint for nonzero transverse exchange: the exchange connects all spin-word fragments within a fixed (N_\uparrow,N_\downarrow) sector and drives the system toward the complete fixed-charge-sector state. However, the finite-size convergence proof does not provide a system-size-independent relaxation time or spectral-gap estimate.

The static analysis classifies typical fixed-composition words, which lack long-range nonlinear order in any fixed finite-support charged channel, and periodic words, whose primitive period determines the minimum support and allowed composite strong-to-weak symmetry-breaking channels. The authors leave unresolved both the scaling of dynamical relaxation with L and J_\perp and the corresponding classification for more general nonperiodic words.