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Polynomial filter diagonalization of large Floquet unitary operators

by David J. Luitz

Submission summary

As Contributors:	David J. Luitz
Preprint link:	scipost_202106_00028v1
Date accepted:	2021-07-09
Date submitted:	2021-06-16 21:54
Submitted by:	Luitz, David J.
Submitted to:	SciPost Physics
Academic field:	Physics
Specialties:	Quantum Physics
Approach:	Computational

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 $L$ 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 $\geq 10^6$.

Published as SciPost Phys. 11, 021 (2021)

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