Affiliation:
1. Max Planck Institute for the Physics of Complex Systems
Abstract
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
LL
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 \geq 10^6≥106.
Funder
Deutsche Forschungsgemeinschaft
Subject
General Physics and Astronomy
Cited by
3 articles.
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