Exact Mazur bounds in the pair-flip model and beyond

TL;DR

This paper derives exact bounds on spin autocorrelation functions in pair-flip models, revealing that nontrivial conservation laws significantly affect thermalization, with autocorrelations exhibiting infinite coherence times at boundaries and a decay rate of 1/√L in the bulk.

Contribution

It provides the first exact analytical results for Mazur bounds in pair-flip models, demonstrating the impact of conservation laws on thermalization beyond simple symmetries.

Findings

Autocorrelation functions have infinite coherence times at boundaries.

Bulk Mazur bounds decay as 1/√L, not 1/L.

Nontrivial conserved operators influence thermalization properties.

Abstract

By mapping the calculation of Mazur bounds to the enumeration of walks on fractal structures, we present exact bounds on the late-time behavior of spin autocorrelation functions in models exhibiting pair-flip dynamics and more general $p$-flip dynamics. While the pair-flip model is known to exhibit strong Hilbert space fragmentation, the effect of its nontrivial conservation laws on autocorrelation functions has, thus far, only been calculated numerically, which has led to incorrect conclusions about their thermodynamic behavior. Here, using exact results, we prove that infinite-temperature autocorrelation functions exhibit infinite coherence times at the boundary, and that bulk Mazur bounds decay asymptotically as $1/\sqrt{L}$, rather than $1/L$, as had previously been thought. This result implies that the nontrivial conserved operators implied by $p$-flip dynamics have an important qualitative impact on bulk thermalization properties beyond the constraints imposed by the simple global symmetries of the models.