TY - JOUR
T1 - Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model
AU - Zhao, Hui Hai
AU - Ido, Kota
AU - Morita, Satoshi
AU - Imada, Masatoshi
N1 - Funding Information:
We would like to thank Naoki Kawashima, Frank Pollmann, and Ying-Jer Kao for stimulating discussion. The authors thank the Supercomputer Center, Institute for Solid State Physics, University of Tokyo, for the facilities. This work was financially supported by the Japan Society for the Promotion of Science through the Program for Leading Graduate Schools (MERIT), the MEXT HPCI Strategic Programs for Innovative Research (SPIRE), Computational Materials Science Initiative (CMSI), and Creation of New Functional Devices and High-Performance Materials to Support Next-Generation Industries (CDMSI). We are thankful for the computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research project (under Projects No. hp130007, No. hp140215, No. hp150211, and No. hp160201). This work was also supported by Grants-in-Aid for Scientific Research (No. 22104010, No. 22340090, and No. 16H06345) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
Publisher Copyright:
© 2017 American Physical Society.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study fermionic models. The variational wave function is composed of a pair product wave function operated by real-space correlation factors and tensor networks. Moreover, we can apply quantum number projections, such as spin, momentum, and lattice symmetry projections, to recover the symmetry of the wave function to further improve the accuracy. We benchmark our method for one- and two-dimensional Hubbard models, which show significant improvement over the results obtained individually either by mVMC or by tensor network. We have applied the present method to a hole-doped Hubbard model on the square lattice, which indicates the stripe charge/spin order coexisting with a weak d-wave superconducting order in the ground state for the doping concentration of less than 0.3, where the stripe oscillation period gets longer with increasing hole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excited state for the doping concentration less than 0.25.
AB - The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study fermionic models. The variational wave function is composed of a pair product wave function operated by real-space correlation factors and tensor networks. Moreover, we can apply quantum number projections, such as spin, momentum, and lattice symmetry projections, to recover the symmetry of the wave function to further improve the accuracy. We benchmark our method for one- and two-dimensional Hubbard models, which show significant improvement over the results obtained individually either by mVMC or by tensor network. We have applied the present method to a hole-doped Hubbard model on the square lattice, which indicates the stripe charge/spin order coexisting with a weak d-wave superconducting order in the ground state for the doping concentration of less than 0.3, where the stripe oscillation period gets longer with increasing hole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excited state for the doping concentration less than 0.25.
UR - http://www.scopus.com/inward/record.url?scp=85029502721&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85029502721&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.96.085103
DO - 10.1103/PhysRevB.96.085103
M3 - Article
AN - SCOPUS:85029502721
VL - 96
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
SN - 2469-9950
IS - 8
M1 - 085103
ER -