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Nonlinear optical (NLO) effects in materials with band crossings have attracted significant research interests due to the divergent band geometric quantities around these crossings. Most current research has focused on band crossings between the valence and conduction bands. However, such crossings are absent in insulators, which are more relevant for NLO applications. In this work, we demonstrate that NLO effects can be significantly enhanced by band crossings within the valence or conduction bands, which we designate as "deep band crossings" (DBCs). As an example, in two dimensions, we show that shift conductivity can be substantially enhanced or even divergent due to a mirror-protected "deep Dirac nodal point". In three dimensions, we propose GeTe as an ideal material where shift conductivity is enhanced by "deep Dirac nodal lines". The ubiquity of this enhancement is further confirmed by high-throughput calculations. Other types of DBCs and NLO effects are also discussed. By manipulating band crossings between arbitrary bands, our work offers a simple, practical, and universal way to greatly enhance NLO effects.

Ab initio modeling of conical intersection dynamics is crucial for various photochemical, photophysical, and biological processes. However, adiabatic electronic states obtained from electronic structure computations involve random phases, or more generally, random gauge fixings, which hampers the modeling of nonadiabatic molecular dynamics. Here we develop a random-gauge local diabatic representation that allows an exact modeling of conical intersection dynamics directly using the adiabatic electronic states with phases randomly assigned during the electronic structure computations. Its utility is demonstrated by an exact ab initio modeling of the two-dimensional Shin-Metiu model with and without an external magnetic field. Our results provide a simple approach to integrating the electronic structure computations into non-adiabatic quantum dynamics, thus paving the way for ab initio modeling of conical intersection dynamics.

We develop and implement an exact conical intersection nonadiabatic wave packet dynamics method that combines the local diabatic representation, Strang splitting for the total molecular propagator, and discrete variable representation with uniform grids. By employing the local diabatic representation, this method captures all non-adiabatic effects, including nonadiabatic transitions, electronic coherences, and geometric phases. Moreover, it is free of singularities in the first and second derivative couplings, and does not require a smooth gauge of electronic wavefunction phase. We further show that in contrast to the adiabatic representation, the split-operator method can be directly applied to the full molecular propagator with the locally diabatic ansatz. The Fourier series, employed as the primitive nuclear basis functions, is universal and can be applied to all types of reactive coordinates. The combination of local diabatic representation, Strang splitting, and Fourier basis allows exact modeling of conical intersection quantum dynamics directly with adiabatic electronic states that can be obtained from standard electronic structure computations.

The time-convolutionless master equation provides a general framework to model non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative expansion of the exact time-local generator for an open quantum system interacting with arbitrary environments. A truncation of the perturbation expansion leads to the perturbative time-convolutionless quantum master equations. We further introduce a nonperturbative approach that approximates the time-convolutionless generator as a nested time-ordered exponential function.

Chiral magnetic states in two-dimensional (2D) layered noncentrosymmetric magnets, which are promising advanced spintronic materials, are usually attributed to Dzyaloshinskii-Moriya interactions (DMI). However, the role of underlying higher-order spin couplings in determining the properties of chiral spin textures has much less reported. In this work, taking the lithium-decorated monolayer CrTe$_{2}$ (monolayer LiCrTe$_{2}$) as an example, we develop a first-principles-based comprehensive spin model constructed by using the symmetry-adapted cluster expansion method. Based on this spin model, we identify the ground state of monolayer LiCrTe$_{2}$ as a chiral spin spiral state, which can further assemble macroscopic chiral labyrinth domains (LD) under zero-field conditions as well as evolve into skyrmions under a finite magnetic field. Moreover, higher-order biquadratic and three-site interactions are identified to be responsible for modulating both the size and the field stability of the spin spiral state. Our study sheds light on complex magnetic couplings in 2D magnets., Comment: 10 pages, 5 figures

Strong light-matter coupling provides a versatile and novel means to manipulate chemical processes. Here we develop a theoretical framework to investigate the spectroscopy and dynamics of a molecular ensemble embedded in an optical cavity under the collective strong coupling regime. This theory is constructed by a pseudoparticle representation of the molecular Hamiltonians, mapping the polaritonic Hamiltonian into a coupled fermion-boson model under particle number constraints. The mapped model is then analyzed using the non-equilibrium Green function theory with the important self-energy diagrams identified through power counting. Numerical demonstrations are shown for the driven Tavis-Cummings model, which shows an excellent agreement with exact results.

Recent advances in laser technology now enable engineering the electronic structure of matter through strong light-matter interactions. However, the effective physicochemical properties of these laser-dressed nonequilibrium materials are not well understood. Here we develop a general theory that now enables modeling and interpreting the linear optical absorption of solids that are dressed by light of arbitrary strength and photon energy. The theory applies to any crystalline solid and quantum materials. In the theory, the dressing of Bloch electrons by the driving laser is treated exactly using Floquet theory. The effective optical properties of this laser-dressed material are probed through a weak laser whose effects are captured to first order in perturbation theory. Remarkably, in this nonequilibrium system the time- and space-periodic Floquet-Bloch modes play the role of the pristine eigenstates of matter as the optical absorption is seen to emerge from transitions among them. We implement the theoretical framework into a code FloqticS: Floquet optics in Solids) available through Github. To isolate the emergent phenomenology, we performed computations in a model solid with a cosine-shaped lattice potential driven by strong nonresonant light. The computations recover the dynamical Franz-Keldysh effect and identify novel dramatic changes in the optical absorption upon increasing the amplitude of the driving laser. The Floquet replicas open absorption sidebands separated by integer multiples of the drive photon energy. The hybridization of the Floquet-Bloch modes, create intense low-frequency absorption and stimulated emissions, and dips in the absorption spectrum. We assign these emerging effects as purely-optical tell-tale signatures of the Floquet-Bloch modes. These advances can be used to model, control and characterize the response properties of laser-dressed materials.

Conical intersections are ubiquitous in polyatomic molecules and responsible for a wide range of phenomena in chemistry and physics. We introduce and implement a local diabatic representation for the correlated electron-nuclear dynamics around conical intersections. It employs the adiabatic electronic states but avoids the singularity of nonadiabatic couplings, and is robust to different gauge choices of the electronic wavefunction phases. Illustrated by a two-dimensional conical intersection model, this representation captures nonadiabatic transitions, electronic coherence, and geometric phase.

Light-driven matter can exhibit qualitatively distinct electronic and optical properties from those observed at equilibrium. We introduce generalized sum rules for the optical properties of driven systems by both quantum and classical light. For classical light, it shows that the sum of all Fourier components, indexed by n, of the time-dependent dipole matrix elements between dressed states weighted by the corresponding quasienergy difference in the first Floquet Brillouin zone plus n driving frequency is a constant, determined by the number of electrons. An analogous sum rule for quantum light-dressing is also derived. These developments provide guidance for the control of effective optical properties of matter by light fields.

First-principles calculation of nonlinear magneto-optical effects has become an indispensable tool to reveal the geometric and topological nature of electronic states and to understand light-matter interactions. While intriguingly rich physics could emerge in magnetic materials, further methodological developments are required to deal with time-reversal symmetry breaking, due to the degeneracy and gauge problems caused by symmetry and the low-frequency divergence problem in the existing calculation formalism. Here we present a gauge-covariant and low-frequency convergent formalism for the first-principles computation. Remarkably, this formalism generally works for both non-magnetic and magnetic materials with or without band degeneracy. Reliability and capability of our method are demonstrated by studying example materials (i.e., bilayers of MnBi$_2$Te$_4$ and CrI$_3$) and comparing with published results. Moreover, an importance correction term that ensures gauge covariance of degenerate states is derived, whose influence on physical responses is systematically checked. Our method enables computation of nonlinear magneto-optical effects in magnetic materials and paves the way for exploring rich physics created by the interplay of light and magnetism.

Quantum light spectroscopy, providing novel molecular information non-accessible by classical light, necessitates new computational tools when applied for complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce the entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two-time distribution characteristic of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.

With many frameworks based on message passing neural networks proposed to predict molecular and bulk properties, machine learning methods have tremendously shifted the paradigms of computational sciences underpinning physics, material science, chemistry, and biology. While existing machine learning models have yielded superior performances in many occasions, most of them model and process molecular systems in terms of homogeneous graph, which severely limits the expressive power for representing diverse interactions. In practice, graph data with multiple node and edge types is ubiquitous and more appropriate for molecular systems. Thus, we propose the heterogeneous relational message passing network (HermNet), an end-to-end heterogeneous graph neural networks, to efficiently express multiple interactions in a single model with {\it ab initio} accuracy. HermNet performs impressively against many top-performing models on both molecular and extended systems. Specifically, HermNet outperforms other tested models in nearly 75\%, 83\% and 94\% of tasks on MD17, QM9 and extended systems datasets, respectively. Finally, we elucidate how the design of HermNet is compatible with quantum mechanics from the perspective of the density functional theory. Besides, HermNet is a universal framework, whose sub-networks could be replaced by other advanced models.