An efficient density matrix renormalization group algorithm for chains with periodic boundary condition

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 x 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. Received: 2 August 2016, Accepted: 12 October 2016; Edited by: K. Hallberg; DOI: http://dx.doi.org/10.4279/PIP.080006 Cite as: D Dey, D Maiti, M Kumar, Papers in Physics 8, 080006 (2016)

Keywords

• Periodic boundary conditions
• DMRG