Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems

Wenyuan Liu

We introduce a replica exchange molecular dynamics (MD) optimization algorithm
to obtain the ground state in the representation of tensor network states (TNS), based on the
Monte Carlo sampling techniques, by mapping the energy function of the TNS to that of a
classical mechanical system. The method is expected to effectively avoid local minima of
the
energy functions. We make benchmark tests on a 1D Hubbard model based on matrix
product states (MPS) and a 2D Heisenberg J1-J2 model on a square lattice based on string
bond states (SBS). The results show that the optimization method is robust and efficient
compared to the existing results.