Reduced-density-matrix-based ab initio cavity quantum electrodynamics

TL;DR

This paper introduces a reduced-density-matrix approach for ab initio cavity QED, enabling efficient modeling of light-matter interactions and their effects on electronic properties without full wave function calculations.

Contribution

It develops a novel RDM-based method for cavity QED that enforces ensemble N-representability and applies it to strongly correlated systems with ultrastrong light-matter coupling.

Findings

Cavity can significantly alter the singlet-triplet gap in oligoacenes.

Strong light-matter coupling enhances the insulating behavior in hydrogen chains.

The method achieves polynomial-time optimization without full wave function knowledge.

Abstract

A reduced-density-matrix (RDM)-based approach to {\em ab initio} cavity quantum electrodynamics (QED) is developed. The expectation value of the Pauli-Fierz Hamiltonian is expressed in terms of one- and two-body electronic and photonic RDMs, and the elements of these RDMs are optimized directly in polynomial time by semidefinite programming techniques, without knowledge of the full wave function. QED generalizations of important ensemble $N$-representability conditions are derived and enforced in this procedure. The resulting approach is applied to the description of classic ground-state strong electron correlation problems, augmented by the presence of ultrastrong light-matter coupling. First, we assess cavity-induced changes to the singlet-triplet energy gap of the linear oligoacene series; for a heptacene molecule, this gap can change by as much as 1.9 kcal mol$^{-1}$ (or 15\%) when the molecule is aligned along the cavity mode polarization axis. We also explore the metal-insulator transition in linear hydrogen chains and demonstrate that strong electron-photon interactions increase the insulating character of these systems under all coupling strengths considered.