On the accuracy of the density matrix renormalization group method

TL;DR

This paper evaluates the accuracy of White's density matrix renormalization group method by applying it to the exactly solvable 1D Ising model in a transverse field, analyzing errors in various computed properties.

Contribution

It provides a detailed analysis of the DMRG method's errors using the exactly solvable ITF model, aiding in its optimization for broader applications.

Findings

Errors depend on model and algorithm parameters

Ground-state energies and correlations are accurately computed

Insights help optimize DMRG for other systems

Abstract

White's density matrix renormalization group ({DMRG}) method has been applied to the one-dimensional Ising model in a transverse field ({ITF}), in order to study the accuracy of the numerical algorithm. Due to the exact solubility of the {ITF} for any finite chain length, the errors introduced by the basis truncation procedure could have been directly analysed. By computing different properties, like the energies of the low-lying levels or the ground-state one- and two-point correlation functions, we obtained a detailed picture, how these errors behave as functions of the various model and algorithm parameters. Our experience with the {ITF} contributes to a better understanding of the {DMRG} method, and may facilitate its optimization in other applications.