Variational approach for 1D antiferromagnetic Heisenberg chain with matrix-product states

In order to explore the practical applicability of variational Monte Carlo simulations based on matrix-product states (MPS) [1], we present two implementations for the one-dimensional antiferromagnetic Heisenberg model with periodic boundary conditions [2]. We compare the convergence properties of two different schemes, which use either two sets of matrices corresponding to the two sublattices, or a 2-spin block representation. It is found that the use of symmetries considerably speeds up the convergence with the matrix size D. We also present an efficient ``cooling'' schedule for the stochastic method used to optimize the matrices, which significantly reduces the computational effort. Finally, we will discuss application of the scheme to n-leg ladders with periodic boundary condition. \newline [1] A. W. Sandvik and G. Vidal, arXiv:0708.2232. \newline [2] Y.-J. Kao, L. Wang, and A. W. Sandvik (unpublished)