Infinite-size density matrix renormalization group with parallel Hida's algorithm

Abstract

In this study, we report a parallel algorithm for the infinite-size density matrix renormalization group (iDMRG) that is applicable to one-dimensional (1D) quantum systems with $\ell$-site periods, where $\ell$ is an even number. It combines Hida's iDMRG applied to random 1D spin systems with a variant of McCulloch's wavefunction prediction. This allows us to apply $\ell /2$ times of computational power to accelerate the investigation of multi-leg frustrated quantum systems in the thermodynamic limit, which is a challenging simulation. We performed benchmark calculations for a spin-1/2 Heisenberg model on a Kagome cylinder YC8 using the parallel iDMRG, and found that the proposed iDMRG was efficiently parallelized for shared memory and distributed memory systems, and provided such bulk physical quantities as total energy, bond strength on nearest neighbor spins, and spin--spin correlation functions and their correlation lengths without finite-size effects. Moreover, the variant of the wavefunction prediction sped up Lanczos methods in the parallel iDMRG by approximately three times.

7 pages, 13 figures

References in corpus (4)

• The density-matrix renormalization group in the age of matrix product states
• Real-Space Parallel Density Matrix Renormalization Group
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• DMRG simulations of SU(N) Heisenberg chains using standard Young tableaux: fundamental representation and comparison with finite-size Bethe ansatz

Cited by in corpus (3)

• Parallel time-dependent variational principle algorithm for matrix product states
• Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions
• Automatic Structural Search of Tensor Network States including Entanglement Renormalization