Variational Monte Carlo simulations using tensor-product projected states

Abstract

We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this approach, 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. The entanglement already contained in the input wave function can considerably reduce the bond dimensions compared to the regular tensor-product state representation. In particular, this allows us to also represent states that do not obey the area law of entanglement entropy. In addition, for fermionic systems, the fermion sign structure can be encoded in the input wave function. We show that the optimized states provide good approximations of the ground-state energy and correlation functions in the cases of two-dimensional bosonic and fermonic systems.

7 pages, 5 figures, published version

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• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states
• Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
• Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model
• Generalized Transfer Matrix States from Artificial Neural Networks
• A Projector Quantum Monte Carlo Method for non-linear wavefunctions
• Direct sampling of projected entangled-pair states
• Charge dynamics of correlated electrons: Variational description with inclusion of composite fermions
• Interacting spinless fermions on the square lattice: Charge order, phase separation, and superconductivity
• Combination of Tensor Network States and Green's function Monte Carlo
• Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations
• Gutzwiller Renormalization Group
• All-mode Renormalization for Tensor Network with Stochastic Noise