Energy-filtered excited states and real-time dynamics served in a contour integral

• URL: http://arxiv.org/abs/2409.07354v2
• Date: Fri, 28 Feb 2025 17:58:57 GMT
• Title: Energy-filtered excited states and real-time dynamics served in a contour integral
• Authors: Ke Liao,
• Abstract summary: Cauchy integral formula (CIF) can be used to represent holomorphic functions of diagonalizable operators on a finite domain.<n>I showcase a novel real-time electron dynamics (RT-EOM-CCSD) algorithm based on the CIF form of the exponential time-evolution operator.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: It is observed that the Cauchy integral formula (CIF) can be used to represent holomorphic functions of diagonalizable operators on a finite domain. This forms the theoretical foundation for applying various operators in the form of a contour integral to a state, while filtering away eigen-components that are not included by the contour. As a special case, the identity operator in the integral form--the Riesz projector--is used to design an algorithm for finding a given number of eigen-pairs whose energies are close to a specified value in the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) framework, with applications to calculate core excited states of molecules which is relevant for the X-ray absorption spectroscopy (XAS). As a generalization, I showcase a novel real-time electron dynamics (RT-EOM-CCSD) algorithm based on the CIF form of the exponential time-evolution operator, which admits extremely large time steps while preserving accurate spectral information.

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