Particle-time duality in the kicked Ising spin chain

2016/02/23 by M. Akila, M Akila, D. Waltner +5 · 1 voice · 109 citations
Computer Science · Physics and Astronomy · #Duality (order theory) #Operator (biology) #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Spectrum (functional analysis) #Spin (aerodynamics) #Spins #TRACE (psycholinguistics) #Theoretical and Computational Physics #Unitary operator #Unitary state #cond-mat.stat-mech #nlin.CD #quant-ph

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

published in Journal of Physics A Mathematical and Theoretical 49(37), 375101 (Institute of Physics) · 16 pages, 8 figures

arxiv published 2016/02/23 · arxiv created 2016/02/24 · openalex publication_date 2016/08/19 · openalex created_date 2016/08/23 · arxiv updated 2018/02/07 · openalex updated_date 2026/08/05

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 characterize this dual operator by its spectrum. Using the 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.

Citations

• Random Matrix Theories in Quantum Physics: Common Concepts
• Semiclassical Foundation of Universality in Quantum Chaos
• Spectral form factor near the Ehrenfest time
• General relation between quantum ergodicity and fidelity of quantum dynamics
• Connecting entanglement in time and space: Improving the folding algorithm
• Two soluble models of an antiferromagnetic chain
• Semiclassical theory of spectral rigidity
• Spectral statistics of chaotic many-body systems

Cited by

• Dataset for "Generalized Spectral Statistics in the Kicked Ising model"
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• Discrete time crystals detected by time-translation twist
• Spectral Lyapunov exponents in chaotic and localized many-body quantum systems
• Finding periodic orbits in projected quantum many-body dynamics
• Exact local correlations in kicked chains
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation

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]

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