2014/03/05 by Martin Ganahl, Patrik Thunström, Frank Verstraete +2 · 2 citations
Mathematics · Physics and Astronomy · #Anderson impurity model #Applied mathematics #Chebyshev filter #Chebyshev polynomials #Discretization #Hubbard model #Impurity #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Physics of Superconductivity and Magnetism #Product (mathematics) #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Statistical physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.90.045144
published as Phys. Rev. B 90, 045144 (2014) · 13 pages, 9 figures
arxiv created 2014/03/05 · openalex publication_date 2014/07/30 · arxiv updated 2014/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We improve a recently developed expansion technique for calculating real-frequency spectral functions of any one-dimensional model with short-range interactions, by postprocessing computed Chebyshev moments with linear prediction. This can be achieved at virtually no cost, and in sharp contrast to existing methods based on the dampening of the moments, improves the spectral resolution rather than lowering it. We validate the method for the exactly solvable resonating level model and the single impurity Anderson model. It is capable of resolving sharp Kondo resonances, as well as peaks within the Hubbard bands when employed as an impurity solver for dynamical mean-field theory. Our method works at zero temperature and allows for arbitrary discretization of the bath spectrum. It achieves similar precision as the dynamical density matrix renormalization group, at lower cost. We also propose an alternative expansion, of \mathbb1\ensuremath-exp(\ensuremath-\ensuremathτH) instead of the usual H, which opens the possibility of using established methods for the time evolution of matrix product states to calculate the spectral functions directly.