An efficient algorithm for translationally invariant finite-size periodic lattice systems in one spatial dimension

作者：Shi Qian Qian; Zhou Huan Qiang

来源：Journal of Physics A-Mathematical and Theoretical, 2009, 42(27): 272002.

DOI：10.1088/1751-8113/42/27/272002

We develop an efficient algorithm to find a matrix product state representation of the ground-state wavefunctions for translationally invariant finite-size periodic lattice systems in one spatial dimension. This is based on the observation that the efficient computation of the ground-state energy per site only needs to retain a certain number of the largest eigenvalues of the transfer matrix for a matrix product state, without any sacrifice of accuracy. The computational cost is independent of the system's size, and scales as chi(3) with chi being the truncation dimension. The algorithm is tested for the critical quantum Ising model in a transverse field on a finite-size lattice, with the size as large as 4800 for the truncation dimension 200.

• 出版日期2009-7-10
• 单位重庆大学