Variational Quantum Monte Carlo Simulations with Tensor-Network States
Journal Article

Published: Thursday, November 29, 2007
Citation: Physical Review Letters, Volume 99, Number 220602, Pages 4

Authors (2 total): A. W. Sandvik, G. Vidal

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 renormalization group method scale as ND^5 and ND^6, respectively, for periodic systems.