Further developments in correlator product states: deterministic optimization and energy evaluation

TL;DR

This paper introduces a deterministic, non-variational method for optimizing and evaluating correlator product states (CPS) energies, tested on various lattice models, achieving high accuracy and extending CPS to fermionic systems with Slater determinants.

Contribution

The paper presents a novel deterministic approach for CPS energy evaluation that approximates eigenstates without variational optimization, including fermionic extensions with Slater determinants.

Findings

Reproduces CPS energies within 1% of variational results on lattice models.

Validates the method on spin and fermionic Hubbard models.

Incorporates Slater determinants into CPS for fermionic systems.

Abstract

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.