From density-matrix renormalization group to matrix product states

TL;DR

This paper introduces the DMRG algorithm through the lens of matrix product states, highlighting their advantages, flexibility, and the incorporation of symmetries for improved quantum many-body simulations.

Contribution

It provides a detailed comparison between traditional DMRG and the MPS approach, emphasizing the enhanced capabilities and symmetry utilization in MPS.

Findings

MPS offers greater flexibility than traditional DMRG.

Incorporating symmetries improves computational efficiency.

The paper clarifies the relationship between DMRG and MPS.

Abstract

In this paper we give an introduction to the numerical density matrix renormalization group (DMRG) algorithm, from the perspective of the more general matrix product state (MPS) formulation. We cover in detail the differences between the original DMRG formulation and the MPS approach, demonstrating the additional flexibility that arises from constructing both the wavefunction and the Hamiltonian in MPS form. We also show how to make use of global symmetries, for both the Abelian and non-Abelian cases.