Density matrix renormalization group (DMRG) for cyclic and centrosymmetric linear chains

TL;DR

This paper extends the density matrix renormalization group (DMRG) method to cyclic and centrosymmetric chains, focusing on physical properties of quantum spin systems and Hubbard models, demonstrating high accuracy in diverse 1D systems.

Contribution

It introduces adapted DMRG algorithms for cyclic and centrosymmetric chains, emphasizing physical properties over energy accuracy, applicable to various quantum spin and Hubbard models.

Findings

Algorithms accurately compute edge states in Heisenberg antiferromagnets.

Effective for analyzing quantum phases in frustrated spin chains.

High precision results for extended Hubbard and related models.

Abstract

The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of $N$ sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping constant the dimension of the truncated Hilbert space. DMRG algorithms are adapted to open chains with inversion symmetry at the central site, to cyclic chains and to weakly coupled chains. Physical properties rather than energy accuracy is the motivation. The algorithms are applied to the edge states of linear Heisenberg antiferromagnets with spin $S \ge 1$ and to the quantum phases of a frustrated spin-1/2 chain with exchange between first and second neighbors. The algorithms are found to be accurate for extended Hubbard and related 1D models with charge and spin degrees of freedom.