Replica exchange molecular dynamics optimization of tensor network   states for quantum many-body systems
  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. 
Wenyuan Liu, Chao Wang, Yanbin Li, Yuyang Lao, Yongjian Han, Guang-Can   Guo, Lixin He
cond-mat.str-el