Elucidating Many-Body Effects in Molecular Core Spectra through Real-Time Approaches: Efficient Classical Approximations and a Quantum Perspective

TL;DR

This paper introduces efficient classical approximations and a quantum approach for accurately modeling many-body effects in molecular core spectra, capturing satellite features and quasiparticle properties.

Contribution

It develops truncated TD-dCC methods that retain essential correlation effects and proposes a scalable quantum algorithm for core-hole Green's function simulation.

Findings

Approximate TD-dCC methods closely reproduce exact spectral features.

Hierarchical approaches efficiently capture satellite and quasiparticle effects.

Quantum algorithm offers a scalable route for correlated core-level dynamics.

Abstract

Accurately resolving many-body satellite features in molecular core-level spectra requires theoretical approaches that capture electron correlation both efficiently and systematically. The recently developed time-dependent double coupled-cluster (TD-dCC) ansatz achieves this by combining correlation effects from the N- and (N-1)-electron sectors, but its exact formulation remains computationally demanding. Here we introduce a hierarchy of cost-effective approximate TD-dCC ansatzes derived from truncated Baker-Campbell-Hausdorff (BCH) expansions, which preserve a single-similarity-transformation structure while retaining the essential correlation diagrams responsible for satellite formation. We further develop a detailed component analysis that isolates hole-mediated excitation pathways, which are correlated processes arising from the coupling between ground-state and ionized-state amplitudes. We use it to interpret quasiparticle and satellite features across the hierarchy. Applications to the single-impurity Anderson model and molecular systems (H2O and CH4) demonstrate that the approximate TD-dCC methods closely and efficiently reproduce exact many-body spectral features and quasiparticle weights. In parallel, we construct a fault-tolerant quantum signal processing algorithm for the core-hole Green's function, providing a scalable quantum route for simulating correlated core-level dynamics. Together, these developments establish complementary classical and quantum methodologies for quantitative, many-body-accurate core spectroscopy.