Particle-Time Duality in the Kicked Ising Chain II: Applications to the Spectrum

TL;DR

This paper explores a duality in kicked spin chains that links their dynamics over different dimensions, enabling new insights into their spectral properties and explaining previously observed anomalies.

Contribution

It introduces a duality relation connecting unitary and non-unitary operators in kicked spin chains, revealing new spectral analysis methods and explaining short-time spectral anomalies.

Findings

Derived the oscillating part of the density of states for large spin systems

Explained anomalous short-time behavior of the spectral form factor

Established a duality linking dynamics over different dimensions

Abstract

Previously, we demonstrated that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for $N$ spins at time $T$ is related to one of a non-unitary evolution operator for $T$ spins at time $N$. Using this duality relation we obtain the oscillating part of the density of states for a large number of spins. Furthermore, the duality relation explains the anomalous short-time behavior of the spectral form factor previously observed in the literature.