Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method

TL;DR

This paper evaluates the effectiveness of two sets of approximate N-representability conditions, DQG and DQGT, in accurately modeling electron correlation in one-dimensional and quasi-one-dimensional Hubbard models using the variational two-electron reduced-density-matrix method.

Contribution

It compares the performance of DQG and DQGT conditions in capturing correlation effects, showing DQGT's superiority in modeling strong electron correlations.

Findings

DQGT improves ground-state energy estimates.

DQGT better captures strong correlation effects.

Both conditions work well in weak and strong correlation regimes.

Abstract

Minimizing the energy of an $N$-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions (conditions for the 2-RDM to represent an ensemble $N$-electron quantum system), yields a rigorous lower bound to the ground-state energy in contrast to variational wavefunction methods. We characterize the performance of two sets of approximate constraints, (2,2)-positivity (DQG) and approximate (2,3)-positivity (DQGT) conditions, at capturing correlation in one-dimensional and quasi-one-dimensional (ladder) Hubbard models. We find that, while both the DQG and DQGT conditions capture both the weak and strong correlation limits, the more stringent DQGT conditions improve the ground-state energies, the natural occupation numbers, the pair correlation function, the effective hopping, and the connected (cumulant) part of the 2-RDM. We observe that the DQGT conditions are effective at capturing strong electron correlation effects in both one- and quasi-one-dimensional lattices for both half filling and less-than-half filling.