Polynomial filter diagonalization of large Floquet unitary operators

Periodically driven quantum many-body systems play a central role for our understanding of nonequilibrium phenomena. For studies chaos, thermalization, localization and time crystals, the properties eigenvectors eigenvalues unitary evolution operator, their scaling with physical system size $L$ are interest. While static systems, powerful methods partial diagonalization Hamiltonian were developed, eigenproblem remains daunting. In this paper, we introduce Krylov space method to obtain exact eigenpairs Floquet operator eigenvalue closest target on unit circle. Our is based complex polynomial spectral transformation given by geometric sum, leading rapid convergence Arnoldi algorithm. We demonstrate that much more efficient than shift invert in terms both runtime memory requirements, pushing accessible sizes realm 20 qubits, Hilbert dimensions $\geq 10^6$.