Variational Monte Carlo simulations using tensor-product projected states
Olga Sikora1*, Hsueh-Wen Chang1, Chung-Pin Chou2, Frank Pollmann3, Ying-Jer Kao1
1Department of Physics, National Taiwan University, Taipei, Taiwan
2Beijing Computational Science Research Center, Beijing, China
3Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
* presenting author:Olga Sikora,
Over the past years, the class of tensor-product states has been shown to be a very promising tool to study interacting electron and spin models. We propose an efficient variational approach, which combines the advantages of tensor-product states and conventional trial wave functions such as a Jastrow-type or Hartree-Fock wave function. We apply a projector in the form of a tensor-product operator to an input wave function and optimize the tensor elements via variational Monte Carlo. The entanglement already contained in the input wave function can considerably reduce the bond dimensions required for the tensor-product projector, i.e. computational costs of the simulations. We use our method to investigate several many-body bosonic and fermionic systems on the square lattice, and demonstrate that the optimized states provide good approximations of the ground-state energy and correlation functions.

Keywords: tensor-product states, variational Monte Carlo