Lanczos algorithm with Matrix Product States for dynamical correlation functions

TL;DR

This paper introduces a Lanczos algorithm combined with matrix product states to improve the calculation of dynamical correlation functions, achieving higher accuracy and better convergence than previous DMRG-based methods.

Contribution

The authors implement a Lanczos approach using MPS that overcomes limitations of earlier methods, enhancing accuracy and convergence in dynamical correlation calculations.

Findings

More accurate spectral weights and poles compared to previous methods

Better convergence of the spectral functions

Comparable computational cost to earlier approaches

Abstract

The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this paper we reconsider the oldest approach based on a suitable Lanczos-generated approximate basis and implement it using matrix product states (MPS) for the representation of the basis states. The direct use of matrix product states combined with an ex-post reorthogonalization method allows to avoid several shortcomings of the original approach, namely the multi-targeting and the approximate representation of the Hamiltonian inherent in earlier Lanczos-method implementations in the DMRG framework, and to deal with the ghost problem of Lanczos methods, leading to a much better convergence of the spectral weights and poles. We present results for the dynamic spin structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A comparison to Bethe ansatz results in the thermodynamic limit reveals that the MPS-based Lanczos approach is much more accurate than earlier approaches at minor additional numerical cost.