In (1+1)-dimensional quantum field theory, integrability is typically defined as the existence of an infinite number of local charges of different Lorentz spin, which commute with the Hamiltonian. A well known consequence of integrability is that scattering of particles is elastic and factorizable. These properties are the basis for the bootstrap program, which leads to the exact computation of S-matrices and form factors. We consider periodically-driven field theories, whose stroboscopic time-evolution is described by a Floquet Hamiltonian. It was recently proposed by Gritsev and Polkovnikov that it is possible for some form of integrability to be preserved even in driven systems. If a driving protocol exists such that the Floquet Hamiltonian is integrable (such that there is an infinite number of local and independent charges, a subset of which are parity-even, that commute with it), we show that there are strong conditions on the stroboscopic time evolution of particle trajectories, analogous to S-matrix elasticity and factorization. We propose a new set of axioms for the time evolution of particles which outline a new bootstrap program, which can be used to identify and classify integrable Floquet protocols. We present some simple examples of driving protocols where Floquet integrability is manifest; in particular, we also show that under certain conditions, some integrable protocols proposed by Gritsev and Polkovnikov are solutions of our new bootstrap equations.
Cited by 2
Aaron J. Friedman et al., Integrable Many-Body Quantum Floquet-Thouless Pumps
Phys. Rev. Lett. 123, 170603 (2019) [Crossref]
Axel Cortés Cubero et al., Thermodynamic bootstrap program for integrable QFT’s: form factors and correlation functions at finite energy density
J. High Energ. Phys. 2019, 104 (2019) [Crossref]
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- FP7 People: Marie-Curie Actions (FP7 People) (through Organization: European Commission [EC])