Variational quantum Monte Carlo simulations with tensor-network states
Strongly Correlated Electrons
2009-11-13 v2 Statistical Mechanics
Abstract
We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D*D matrices with D up to 48. The computational cost of our scheme formally scales as ND^3, whereas standard MPS approaches and the related density matrix renromalization group method scale as ND^5 and ND^6, respectively, for periodic systems.
Cite
@article{arxiv.0708.2232,
title = {Variational quantum Monte Carlo simulations with tensor-network states},
author = {A. W. Sandvik and G. Vidal},
journal= {arXiv preprint arXiv:0708.2232},
year = {2009}
}
Comments
4+ pages, 2 figures. v2: improved data, comparisons with exact results, to appear in Phys Rev Lett