Comparison of Variational Approaches for the Exactly Solvable 1/r-Hubbard Chain

TL;DR

This paper compares various variational wave functions for the exactly solvable 1/r-Hubbard model, revealing limitations in their ability to accurately predict the metal-insulator transition in low-dimensional systems.

Contribution

It provides an exact solution for the variational ground state energies of certain wave functions in the 1/r-Hubbard model and evaluates their effectiveness in capturing phase transitions.

Findings

None of the wave functions correctly predict the metal-insulator transition.

The combined Gutzwiller-Baeriswyl wave function is exact in certain limits but fails at finite interactions.

Hartree-Fock and Jastrow-type wave functions are unreliable for zero-temperature phase transitions in low-dimensional systems.

Abstract

We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional $1/r$-Hubbard model. We find that none of these variational wave functions is able to correctly reproduce the physics of the metal-to-insulator transition which occurs in the model for half-filled bands when the interaction strength equals the bandwidth. The many-particle problem to calculate the variational ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave function is exactly solved for the~$1/r$-Hubbard model. The latter wave function becomes exact both for small and large interaction strength, but it incorrectly predicts the metal-to-insulator transition to happen at infinitely strong interactions. We conclude that neither Hartree-Fock nor Jastrow-type wave functions yield reliable predictions on zero temperature phase transitions in low-dimensional, i.e., charge-spin separated systems.