Abstract
We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of matrix product states (MPS), related to the density matrix renormalization group (DMRG) method. It improves on a previous approach by Verstraete et al. We introduce a factorization procedure for long products of MPS matrices, which reduces the computational effort from to , where is the matrix dimension, and in typical cases. We test the method on the and Heisenberg chains. It is also applicable to nontranslationally invariant cases. The method makes ground-state calculations with periodic boundary conditions about as efficient as traditional DMRG calculations for systems with open boundaries.
- Received 30 December 2009
DOI:https://doi.org/10.1103/PhysRevB.81.081103
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