Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions

Author(s): B. Pirvu, F. Verstraete, G. Vidal

Journal: Phys. Rev. B

Volume: 83

Page(s): 125104

Year: 2011

DOI Number: 10.1103/PhysRevB.83.125104

Link: Link to publication


We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain with N sites and correlation length ξ, the computational cost formally scales as g(D,ξ/N)D3, where g(D,ξ/N) is a nontrivial function. For ξ≪N, this scaling reduces to D3, independent of the system size N, making our method N times faster than previous proposals. We apply the algorithm to obtain MPS approximations for the ground states of the critical quantum Ising and Heisenberg spin-1/2 models as well as for the noncritical Heisenberg spin-1 model. In the critical case, for any chain length N, we find a model-dependent bond dimension D(N) above which the polynomial decay of correlations is faithfully reproduced throughout the entire system.

Note: http://arxiv.org/abs/1005.5195

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