Track synthesis, materials and catalysis as it is published.
Search papers, labs, and topics across Lattice.
The authors reformulate the dynamical $G_0W_0$ self-energy by mapping real frequencies onto the unit circle via a Cayley transformation to keep high-order moment constraints strictly bounded. This framework constructs a compact, linearly scaling Hermitian upfolded Hamiltonian from an $O(N^4)$ contour integration, eliminating the need for frequency grids, plasmon-pole approximations, or ill-posed analytic continuation. Across the GW100 benchmark and Chlorophyll A, the resulting single-shot diagonalization yields an explicit full-frequency Green's function with strictly real poles and non-negative spectral weights, achieving substantially faster and more reliable convergence than monomial-moment methods.
Mapping self-energy moments to the unit circle eliminates the notorious instability of high-order moments, enabling grid-free, full-frequency $G_0W_0$ spectra with guaranteed real poles and non-negative spectral weights.
The dynamical GW self-energy approximation is a key computational tool to provide the fundamental spectrum of electronic systems. We reformulate this approximation, representing the particle and hole parts of the GW self-energy through a highly compact set of Cayley-transformed moment constraints. The Cayley transformation maps real frequencies to the unit circle, keeping the moments bounded as their order increases, ensuring numerical stability and allowing resolution to be focused on an energy range of interest. We calculate these Cayley-transformed moments via an efficient O[N$^4$] scaling contour integration, and from them, construct a Hermitian upfolded Hamiltonian with a linearly scaling dimensionality with system size. A single-shot diagonalization of this effective Hamiltonian gives an explicit full-frequency G0W0 Green's function with manifestly real poles and non-negative spectral weights. This enables quasiparticle energies, satellite features, and their spectral weights to be obtained across the full G0W0 spectrum. Comparisons with exact G0W0 calculations and convergence across the GW100 test set and the larger Chlorophyll A molecule demonstrate substantially faster and more reliable convergence with moment order than an earlier monomial-moment approach. These Cayley moment representations therefore provide a stable, compact, and systematically improvable route to the complete spectral information of zero-temperature GW, without explicit frequency grids, plasmon-pole models and other common approximations, or analytic continuation.