The relevance of degenerate states in chiral polaritonics.

In this work, we theoretically explore whether a parity-violating/chiral light-matter interaction is required to capture all relevant aspects of chiral polaritonics or if a parity-conserving/achiral theory is sufficient (e.g., long-wavelength/dipole approximation).

Cavity-enhanced superconductivity in MgB from first-principles quantum electrodynamics (QEDFT).

Strong laser pulses can control superconductivity, inducing nonequilibrium transient pairing by leveraging strong-light matter interaction. Here, we demonstrate theoretically that equilibrium ground-state phonon-mediated superconductive pairing can be affected through the vacuum fluctuating electromagnetic field in a cavity. Using the recently developed ab initio quantum electrodynamical density-functional theory approximation, we specifically investigate the phonon-mediated superconductive behavior of MgB[Formula: see text] under different cavity setups and find that in the strong light-matter coupling regime its superconducting transition temperature T[Formula: see text] can be enhanced at most by [Formula: see text]10% in an in-plane (or out-of-plane) polarized and realistic cavity via photon vacuum fluctuations.

Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling.

We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full nonrelativistic Pauli-Fierz problem of an ensemble of strongly coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation for the electronic structure. Consequently, each individual molecule experiences a self-consistent coupling to the dipoles of all other molecules, which amount to non-negligible values in the thermodynamic limit (large ensembles).

Exchange-only virial relation from the adiabatic connection.

The exchange-only virial relation due to Levy and Perdew is revisited. Invoking the adiabatic connection, we introduce the exchange energy in terms of the right-derivative of the universal density functional w.r.

Exchange energies with forces in density-functional theory.

We propose exchanging the energy functionals in ground-state density-functional theory with physically equivalent exact force expressions as a new promising route toward approximations to the exchange-correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential.

The Structure of the Density-Potential Mapping. Part II: Including Magnetic Fields.

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just one-body particle density. In this Part II of a series of two articles, we aim at clarifying the status of this theorem within different extensions of DFT including magnetic fields. We will in particular discuss current-density-functional theory (CDFT) and review the different formulations known in the literature, including the conventional paramagnetic CDFT and some nonstandard alternatives.

Weakened Topological Protection of the Quantum Hall Effect in a Cavity.

We study the quantum Hall effect in a two-dimensional homogeneous electron gas coupled to a quantum cavity field. As initially pointed out by Kohn, Galilean invariance for a homogeneous quantum Hall system implies that the electronic center of mass (c.m.

Numerically Exact Solution for a Real Polaritonic System under Vibrational Strong Coupling in Thermodynamic Equilibrium: Loss of Light-Matter Entanglement and Enhanced Fluctuations.

The first numerically exact simulation of a full ab initio molecular quantum system (HD) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our numerically exact simulations highlight the absence of zero temperature for the strongly coupled matter and light subsystems, due to cavity-induced noncanonical conditions.

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics.

In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics.

Cavity Born-Oppenheimer Hartree-Fock Ansatz: Light-Matter Properties of Strongly Coupled Molecular Ensembles.

Experimental studies indicate that optical cavities can affect chemical reactions through either vibrational or electronic strong coupling and the quantized cavity modes. However, the current understanding of the interplay between molecules and confined light modes is incomplete. Accurate theoretical models that take into account intermolecular interactions to describe ensembles are therefore essential to understand the mechanisms governing polaritonic chemistry.

The Structure of Density-Potential Mapping. Part I: Standard Density-Functional Theory.

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg-Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg-Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework.

A perspective on ab initio modeling of polaritonic chemistry: The role of non-equilibrium effects and quantum collectivity.

This Perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light-matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling.

Frequency-Dependent Sternheimer Linear-Response Formalism for Strongly Coupled Light-Matter Systems.

The rapid progress in quantum-optical experiments, especially in the field of cavity quantum electrodynamics and nanoplasmonics, allows one to substantially modify and control chemical and physical properties of atoms, molecules, and solids by strongly coupling to the quantized field. Alongside such experimental advances has been the recent development of ab initio approaches such as quantum electrodynamical density-functional theory (QEDFT), which is capable of describing these strongly coupled systems from first principles. To investigate response properties of relatively large systems coupled to a wide range of photon modes, ab initio methods that scale well with system size become relevant.

Making ab initio QED functional(s): Nonperturbative and photon-free effective frameworks for strong light-matter coupling.

Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a nonperturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods.

Erratum: Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions [Phys. Rev. Lett. 123, 037401 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.

Polaritonic Chemistry: Collective Strong Coupling Implies Strong Local Modification of Chemical Properties.

A fundamental question in the field of polaritonic chemistry is whether collective coupling implies local modifications of chemical properties scaling with the ensemble size. Here we demonstrate from first-principles that an impurity present in a collectively coupled chemical ensemble features such locally scaling modifications. In particular, we find the formation of a novel dark state for a nitrogen dimer chain of variable size, whose local chemical properties are altered considerably at the impurity due to its embedding in the collectively coupled environment.

Virial Relations for Electrons Coupled to Quantum Field Modes.

In this work, we present a set of virial relations for many electron systems coupled to both classical and quantum fields, described by the Pauli-Fierz Hamiltonian in dipole approximation and using length gauge. Currently, there is growing interest in solutions of this Hamiltonian because of its relevance for describing molecular systems strongly coupled to photonic modes in cavities and in the possible modification of chemical properties of such systems compared to the ones in free space. The relevance of such virial relations is demonstrated by showing a connection to mass renormalization and by providing an exact way to obtain total energies from potentials in the framework of quantum electrodynamical density functional theory.

Chemistry in Quantum Cavities: Exact Results, the Impact of Thermal Velocities, and Modified Dissociation.

In recent years tremendous progress in the field of light-matter interactions has unveiled that strong coupling to the modes of an optical cavity can alter chemistry even at room temperature. Despite these impressive advances, many fundamental questions of chemistry in cavities remain unanswered. This is also due to a lack of exact results that can be used to validate and benchmark approximate approaches.

Light-Matter Hybrid-Orbital-Based First-Principles Methods: The Influence of Polariton Statistics.

A detailed understanding of strong matter-photon interactions requires first-principle methods that can solve the fundamental Pauli-Fierz Hamiltonian of nonrelativistic quantum electrodynamics efficiently. A possible way to extend well-established electronic-structure methods to this situation is to embed the Pauli-Fierz Hamiltonian in a higher-dimensional light-matter hybrid auxiliary configuration space. In this work we show the importance of the resulting hybrid Fermi-Bose statistics of the polaritons, which are the new fundamental particles of the "photon-dressed" Pauli-Fierz Hamiltonian for systems in cavities.

Relevance of the Quadratic Diamagnetic and Self-Polarization Terms in Cavity Quantum Electrodynamics.

Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light-matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results.

Light-Matter Response in Nonrelativistic Quantum Electrodynamics.

We derive the full linear-response theory for nonrelativistic quantum electrodynamics in the long wavelength limit and provide a practical framework to solve the resulting equations by using quantum-electrodynamical density-functional theory. We highlight how the coupling between quantized light and matter changes the usual response functions and introduces cross-correlated light-matter response functions. These cross-correlation responses lead to measurable changes in Maxwell's equations due to the quantum-matter-mediated photon-photon interactions.

Reduced Density-Matrix Approach to Strong Matter-Photon Interaction.

We present a first-principles approach to electronic many-body systems strongly coupled to cavity modes in terms of matter-photon one-body reduced density matrices. The theory is fundamentally nonperturbative and thus captures not only the effects of correlated electronic systems but accounts also for strong interactions between matter and photon degrees of freedom. We do so by introducing a higher-dimensional auxiliary system that maps the coupled fermion-boson system to a dressed fermionic problem.

Force balance approach for advanced approximations in density functional theories.

We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead, it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent settings.

Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields.

We propose a solution to the problem of Bloch electrons in a homogeneous magnetic field by including the quantum fluctuations of the photon field. A generalized quantum electrodynamical (QED)-Bloch theory from first principles is presented. In the limit of vanishing quantum fluctuations, we recover the standard results of solid-state physics: the fractal spectrum of the Hofstadter butterfly.