Variational Monte Carlo simulations using tensor-product projected states

Olga Sikora, Hsueh-Wen Chang, Chung-Pin Chou, Frank Pollmann, and Ying-Jer Kao

We present a variational Monte Carlo method, which combines the advantages of recently developed 
tensor-product states and conventional trial wave functions. We apply a projector in the form of a 
tensor-product operator to an input wave function, such as a Jastrow-type or Hartree-Fock wave 
function, and optimize the tensor elements via variational Monte Carlo. Choosing an input state 
containing some features of the ground state 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.