Spectral decomposition and high-accuracy Greens functions: Overcoming the Nyquist-Shannon limit via complex-time Krylov expansion

• URL: http://arxiv.org/abs/2411.09680v1
• Date: Thu, 14 Nov 2024 18:45:59 GMT
• Title: Spectral decomposition and high-accuracy Greens functions: Overcoming the Nyquist-Shannon limit via complex-time Krylov expansion
• Authors: Sebastian Paeckel,
• Abstract summary: We show how a fundamental limitation can be overcome using complex-time Krylov spaces. At 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The accurate computation of low-energy spectra of strongly correlated quantum many-body systems, typically accessed via Greens-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 $\Delta\omega$ according to the numerically accessible time domain size $T$ via $\Delta\omega = 2/T$. 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 quasi-particle velocities. Here, we show how this fundamental limitation can be overcome using complex-time Krylov spaces. At 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.

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