High order non-unitary split-step decomposition of unitary operators

Abstract

We propose a high order numerical decomposition of exponentials of hermitean operators in terms of a product of exponentials of simple terms, following an idea which has been pioneered by M. Suzuki, however implementing it for complex coefficients. We outline a convenient fourth order formula which can be written compactly for arbitrary number of noncommuting terms in the Hamiltonian and which is superiour to the optimal formula with real coefficients, both in complexity and accuracy. We show asymptotic stability of our method for sufficiently small time step and demonstrate its efficiency and accuracy in different numerical models.

10 pages, 4 figures (5 eps files) Submitted to J. of Phys. A: Math. Gen

References in corpus (5)

• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
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