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($p\times m^3$), 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.

7 pages, 4 figures

References in corpus (11)

• Topological insulators and superconductors
• The density-matrix renormalization group in the age of matrix product states
• DMRG and periodic boundary conditions: a quantum information perspective
• Computational Studies of Quantum Spin Systems
• New Trends in Density Matrix Renormalization
• Multi-magnon bound states in the frustrated ferromagnetic 1D chain
• Efficient Matrix Product State Method for periodic boundary conditions
• Tuning the bond order wave (BOW) phase of half-filled extended Hubbard models
• Numerical study of incommensurate and decoupled phases of spin-1/2 chains with isotropic exchange J1, J2 between first and second neighbors
• Stiffness in 1D Matrix Product States with periodic boundary conditions
• Spin-supersolid phase in Heisenberg chains: a characterization via Matrix Product States with periodic boundary conditions

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