An Efficient Density Matrix Renormalization Group Algorithm for Chains with Periodic Boundary Condition

TL;DR

This paper introduces a new DMRG algorithm for one-dimensional quantum systems with periodic boundary conditions that achieves high accuracy with reduced computational effort, making it comparable to MPS-based methods.

Contribution

A novel DMRG algorithm that matches MPS accuracy for PBC systems while reducing computational complexity to O(m^3).

Findings

Achieves accuracy comparable to MPS algorithms.

Reduces computational effort from O(p×m^3) to O(m^3).

Easily adaptable from conventional DMRG code.

Abstract

The Density Matrix Renormalization Group (DMRG) is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC) from the conventional DMRG has been a challenging job from the inception of DMRG. The recent development of the Matrix Product State (MPS) algorithm gives a new approach to find accurate results for the one dimensional PBC system. The most efficient implementation of the MPS algorithm can scale as O($p \times m^3$), where $p$ can vary from 4 to $m^2$. In this paper, we propose a new DMRG algorithm, which is very similar to the conventional DMRG and gives comparable accuracy to that of MPS. The computation effort of the new algorithm goes as O($m^3$) and the conventional DMRG code can be easily modified for the new algorithm.