Mechanism of the size-independent dip time in spin chains

Determine the precise mechanism by which a Gaussian density of states in spin-chain models produces a spectral-form-factor dip time that remains independent of system size.

Background

The review reports that, for the mixed-field Ising and Heisenberg XXZ spin-chain models, the spectral-form-factor dip time is of order one while the plateau time scales with the Hilbert-space dimension. This differs from random-matrix predictions, where the dip time scales as the square root of the Hilbert-space dimension. The authors attribute the discrepancy plausibly to the Gaussian rather than semicircular density of states but explicitly leave the underlying mechanism unresolved.

References

The precise mechanism by which a Gaussian DOS leads to a size-independent dip time remains an open question for further investigation.

— Quantum Chaos and Spread of States in Krylov Subspace: A Topical Review  (2608.26825 - Jeong et al., 27 Aug 2026) in Section 4.1, subsection “Spectral form factor and time-scale analysis”