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Nonstochastic algorithms for Jastrow-Slater and correlator product state wave functions

2011; American Physical Society; Volume: 84; Issue: 20 Linguagem: Inglês

10.1103/physrevb.84.205132

1550-235X

Eric Neuscamman, Hitesh J. Changlani, Jesse Kinder, Garnet Kin‐Lic Chan,

Quantum and electron transport phenomena

Correlator product states (CPS) are a class of tensor network wavefunctions applicable to strongly correlated problems in arbitrary dimensions. Here, we present a method for optimizing and evaluating the energy of the CPS wavefunction that is non-variational but entirely deterministic. The fundamental assumption underlying our technique is that the CPS wavefunction is an exact eigenstate of the Hamiltonian, allowing the energy to be obtained approximately through a projection of the Schr\"odinger equation. The validity of this approximation is tested on two dimensional lattices for the spin-1/2 antiferromagnetic Heisenberg model, the spinless Hubbard model, and the full Hubbard model. In each of these models, the projected method reproduces the variational CPS energy to within 1%. For fermionic systems, we also demonstrate the incorporation of a Slater determinant reference into the ansatz, which allows CPS to act as a generalization of the Jastrow-Slater wavefunction.