# 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.