2007/08/31 by Anders W. Sandvik, A. W. Sandvik, Guifré Vidal +1 · 3 citations
Mathematics · Physics and Astronomy · #Boundary value problem #Condensed matter physics #Density matrix renormalization group #Diffusion Monte Carlo #Ising model #Markov chain Monte Carlo #Mathematics #Monte Carlo method #Monte Carlo molecular modeling #Periodic boundary conditions #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum many-body systems #Quantum mechanics #Renormalization group #Spins #Statistical physics #Tensor (intrinsic definition) #Tensor product #Theoretical and Computational Physics #Variational Monte Carlo #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.99.220602
4+ pages, 2 figures. v2: improved data, comparisons with exact results, to appear in Phys Rev Lett
arxiv created 2007/10/19 · openalex publication_date 2007/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 x D matrices with D up to 48. The computational cost of our scheme formally scales as ND3, whereas standard MPS approaches and the related density matrix renormalization group method scale as ND5 and ND6, respectively, for periodic systems.