  The tensor network states (TNS) methods combined with Monte Carlo (MC)
techniques have been proved a powerful algorithm for simulating quantum
many-body systems. However, because the ground state energy is a highly
non-linear function of the tensors, it is easy to get stuck in local minima
when optimizing the TNS of the simulated physical systems. To overcome this
difficulty, we introduce a replica-exchange molecular dynamics optimization
algorithm to obtain the TNS ground state, based on the MC sampling techniques,
by mapping the energy function of the TNS to that of a classical dynamical
system. The method is expected to effectively avoid local minima. We make
benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and
a Heisenberg $J_1$-$J_2$ model on square lattice based on string bond states
(SBS). The results show that the optimization method is robust and efficient
compared to the existing results.
