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

Wen Liu, Yanbin Li, Yuyang Lao, Yongjian Han, Guang-Can Guo, Lixin He,

    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.