Polynomial filter diagonalization of large Floquet unitary operators

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 $\ge 10^6$.

4 pages, 4 figures, 1 table

References in corpus (12)

• Thermalization and its mechanism for generic isolated quantum systems
• Many-body localization edge in the random-field Heisenberg chain
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Absence of Quantum Time Crystals
• Dynamical obstruction to localization in a disordered spin chain
• Can we study the many-body localisation transition?
• Absence of true localization in many-body localized phases
• A Brief History of Time Crystals
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Is there slow particle transport in the MBL phase?
• (Quasi)Periodic revivals in periodically driven interacting quantum systems

Cited by in corpus (12)

• Avalanches and many-body resonances in many-body localized systems
• Many-Body Localization in the Age of Classical Computing
• Stability of many-body localization in Floquet systems
• Quantifying quantum chaos through microcanonical distributions of entanglement
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Localization and integrability breaking in weakly interacting Floquet circuits
• Quantum logarithmic multifractality
• DanceQ: High-performance library for number-conserving bases
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Orthogonal layers of parallelism in large-scale eigenvalue computations
• Critical Dynamics of the Anderson Transition on Small-World Graphs
• Anomalous transport in U(1)-symmetric quantum circuits