Spectral Decomposition and High-Accuracy Green’s Functions: Overcoming the Nyquist-Shannon Limit via Complex-time Krylov Expansion

The accurate computation of low-energy spectra of strongly correlated quantum many-body systems, typically accessed via Green’s functions, is a long-standing problem posing enormous challenges to numerical methods. When the spectral decomposition is obtained from Fourier transforming a time series, the Nyquist-Shannon theorem limits the frequency resolution Δ ω according to the numerically accessible time domain size T via Δ ω = 2 π / T . In tensor network methods, increasing the domain size is exponentially hard due to the ubiquitous spread of correlations, limiting the frequency resolution and thereby restricting this ansatz class mostly to one-dimensional systems with small quasiparticle velocities. Here, we show how this limitation can be overcome by augmenting the time series with complex-time Krylov states. With the example of the critical S − 1 / 2 Heisenberg model and light bipolarons in the two-dimensional Su-Schrieffer-Heeger model, we demonstrate the enormous improvements in accuracy, which can be achieved using this method.