Particle-Time Duality in the Kicked Ising Chain I: The Dual Operator

2016/02/23 by M. Akila, D. Waltner, B. Gutkin +1 · 1 voice · 4 citations
Physics and Astronomy · #nlin.CD #quant-ph

paper · pdf · doi:10.1088/1751-8113/49/37/375101

Abstract

We demonstrate 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. We investigate the spectrum of this dual operator with a focus on the different parameter regimes (chaotic, regular) of the spin chain. We present applications of this duality relation to spectral statistics in an accompanying paper.

Cited by

• Dataset for "Generalized Spectral Statistics in the Kicked Ising model"
• Extreme value statistics and eigenstate thermalization in kicked quantum chaotic spin-1/2 chains
• Walsh-Floquet Theory of Periodic Kick Drives
• Mixed state deep thermalization

Discussions

• Consider Kicked field Ising model Hamiltonian given as follows. (I am following the this paper , relevant calculations are in appendix A.) $$ H_I=2 J \sum_k\left[\cos k\left(\hat{b}_k^{\dagger} \hat{b [stackexchange, 3 points]