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

Authors

  • Dayasindhu Dey S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
  • Debasmita Maiti S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India
  • Manoranjan Kumar S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India

DOI:

https://doi.org/10.4279/pip.080006

Keywords:

Periodic boundary conditions, DMRG

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×m3), where p can vary from 4 to m2. 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(m3) 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)

This paper, by D Dey, D Maiti, M Kumar, is licensed under the Creative Commons Attribution License 3.0.

 

Traditional Review

Published

2016-11-18

How to Cite

Dey, D., Maiti, D., & Kumar, M. (2016). An efficient density matrix renormalization group algorithm for chains with periodic boundary condition. Papers in Physics, 8, 080006. https://doi.org/10.4279/pip.080006

Issue

Section

Articles