Necessary N-representability Constraints from Time-reversal Symmetry for Periodic Systems

TL;DR

This paper introduces necessary constraints based on time-reversal symmetry to improve the accuracy of variational 2-RDM calculations in periodic systems, ensuring correct energies without losing computational efficiency.

Contribution

The authors derive and implement linear time-reversal symmetry constraints for 2-RDM in periodic systems, addressing a gap in existing methods.

Findings

Time-reversal symmetry constraints improve energy accuracy in periodic 2-RDM calculations.

Constraints preserve block-diagonal structure from translational invariance.

Validated on metallic hydrogen chain and lithium hydride crystal.

Abstract

The variational calculation of the two-electron reduced density matrix (2-RDM) is extended to periodic molecular systems. If the 2-RDM theory is extended to the periodic case without consideration of time-reversal symmetry, however, it can yields energies that are significantly lower than the correct energies. We derive and implement linear constraints that enforce time-reversal symmetry on the 2-RDM without destroying its computationally favorable block-diagonal structure from translational invariance. Time-reversal symmetry is distinct from space-group or spin (SU(2)) symmetries which can be expressed by unitary transformations. The time-reversal symmetry constraints are demonstrated through calculations of the metallic hydrogen chain and the one-dimensional lithium hydride crystal.