2018/04/30 by Axel Cortés Cubero, Axel Cortes Cubero · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Axiom #Computation #Eigenfunction #Factorization #Floquet theory #Hamiltonian (control theory) #Integrable system #Lorentz transformation #Quantum chaos and dynamical systems #Quantum many-body systems #Unitarity #cond-mat.stat-mech #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.21468/scipostphys.5.3.025
published in SciPost Physics 5(3) (SciPost.org) · 45 pages, 10 figures, typos corrected, improved discussion, references added
openalex created_date 2018/05/07 · arxiv created 2018/07/30 · openalex publication_date 2018/09/21 · arxiv updated 2018/09/26 · openalex updated_date 2026/08/05
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.