Chapter 7 - DMRG in frequency space

Abstract

Spectral function is of central importance in both quantum chemistry and condensed matter physics, as frequency-dependent dynamical properties can be obtained experimentally such as linear absorption and emission spectroscopy, photoelectron spectroscopy, optical conductivity, etc. Thus, for evaluating frequency-dependent dynamical properties, the calculation of dynamical quantities in the frequency domain has also been elaborated through the framework of density matrix renormalization group (DMRG). The major advantage of frequency-domain algorithm over time-dependent simulations is to avoid the error accumulation due to the time evolution. In this chapter, we first present a pedagogical introduction to the linear response theory and the formulation of spectral function at zero and finite temperature. Then, the algorithms for frequency-domain DMRG, including correction vector DMRG, dynamical DMRG, Lanczos DMRG, and Chebyshev matrix product states are introduced. Finally, some representative applications of calculating the dynamical quantities of electron–phonon coupled molecular aggregate, electronic and spin systems by frequency-domain DMRG are discussed.