2021/02/28 by David J. Luitz
Mathematics · Physics and Astronomy · #Eigenvalues and eigenvectors #Floquet theory #Hamiltonian (control theory) #Hilbert space #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Operator (biology) #Physics #Quantum #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum mechanics #Unitary matrix #Unitary operator #Unitary state #Unitary transformation #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.21468/scipostphys.11.2.021
published as SciPost Phys. 11, 021 (2021) · 4 pages, 4 figures, 1 table
arxiv created 2021/07/19 · openalex publication_date 2021/08/03 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Periodically driven quantum many-body systems play a central role for our understanding of nonequilibrium phenomena. For studies of quantum chaos, thermalization, many-body localization and time crystals, the properties of eigenvectors and eigenvalues of the unitary evolution operator, and their scaling with physical system size L <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>L</mml:mi> </mml:math> are of interest. While for static systems, powerful methods for the partial diagonalization of the Hamiltonian were developed, the unitary eigenproblem remains daunting. % In this paper, we introduce a Krylov space diagonalization method to obtain exact eigenpairs of the unitary Floquet operator with eigenvalue closest to a target on the unit circle. Our method is based on a complex polynomial spectral transformation given by the geometric sum, leading to rapid convergence of the Arnoldi algorithm. We demonstrate that our method is much more efficient than the shift invert method in terms of both runtime and memory requirements, pushing the accessible system sizes to the realm of 20 qubits, with Hilbert space dimensions ≥ 106 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>≥</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>6</mml:mn> </mml:msup> </mml:mrow> </mml:math> .