Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group

TL;DR

This paper introduces an adaptive Lanczos-vector method within the density-matrix renormalization group framework to accurately and efficiently compute spectral functions, overcoming limitations of broadening and resolution in existing methods.

Contribution

The paper presents a novel adaptive Lanczos-vector approach for spectral function calculation in DMRG, enabling precise, direct extraction of spectral weights and poles without artificial broadening.

Findings

High accuracy spectral functions obtained efficiently

Direct extraction of spectral weights and poles

Comparison shows improved resolution over correction-vector method

Abstract

Current widely-used approaches to calculate spectral functions using the density-matrix renormalization group in frequency space either necessarily include an artificial broadening (correction-vector method) or have limited resolution (time-domain density-matrix renormalization group with Fourier transform method). Here we propose an adaptive Lanczos-vector method to calculate the coefficients of a continued fraction expansion of the spectral function iteratively. We show that one can obtain a very accurate representation of the spectral function very efficiently, and that one can also directly extract the spectral weights and poles for the discrete system. As a test case, we study spinless fermions in one dimension and compare our approach to the correction vector method.