Blind deconvolution of density-matrix renormalization-group spectra

Abstract

We present a numerical method for calculating piecewise smooth spectral functions of correlated quantum systems in the thermodynamic limit from the spectra of finite systems computed using the dynamical or correction-vector density-matrix renormalization group method. The key idea is to consider this problem as a blind deconvolution with an unknown kernel which causes both a broadening and finite-size corrections of the spectrum. In practice, the method reduces to a least-square optimization under non-linear constraints which enforce the positivity and piecewise smoothness of spectral functions. The method is demonstrated on the single-particle density of states of one-dimensional paramagnetic Mott insulators represented by the half-filled Hubbard model on an open chain. Our results confirm that the density of states has a step-like shape but no square-root singularity at the spectrum onset.