Publications

Lithium-containing molecules, such as C2H2Li2, C6Li6, and several lithium halides, have been studied in the present paper, and the nature of lithium bonds in these structures is investigated. In contrast to the hydrogen bond, which features a typical quasi-linear and dicoordinated (X···H–Y) geometry, the ionic lithium bond prefers nonlinear and multicoodinated geometrical arrangements. On the basis of these observations, we have predicted some novel energetically low-lying C6Li6 structures. With its unusual features, the Li bond theory should be applied rather widely.

We compute the scrambling rate at the antiferromagnetic (AFM) quantum critical point, using the fixed point theory found by Schlief, Lunts, and Lee [Phys. Rev. X 7, 021010 (2017)]. At this strongly coupled fixed point, there is an emergent control parameter w≪1 that is a ratio of natural parameters of the theory. The strong coupling is unequally felt by the two degrees of freedom: the bosonic AFM collective mode is heavily dressed by interactions with the electrons, while the electron is only marginally renormalized. We find that the scrambling rates act as a measure of the “degree of integrability” of each sector of the theory: the Lyapunov exponent for the boson λ(B)L∼O(√w)kBT/ℏ
is significantly larger than the fermion one λ(F)L∼O(w2)kBT/ℏ, where T is the temperature. Although the interaction strength in the theory is of order unity, the larger Lyapunov exponent is still parametrically smaller than the universal upper bound of
λL=2πkBT/ℏ. We also compute the spatial spread of chaos by the boson operator, whose low-energy propagator is highly nonlocal. We find that this nonlocality leads to a scrambled region that grows exponentially fast at intermediate distances, giving an infinite “butterfly velocity” of the chaos front, a result that has also been found in lattice models with long-range interactions.

Dippers are a common class of young variable star exhibiting day-long dimmings with depths of up to several tens of percent. A standard explanation is that dippers host nearly edge-on (70 deg) protoplanetary discs that allow close-in (10 au) disc resolved by ALMA and that inner disc misalignments may be common during the protoplanetary phase. More than one mechanism may contribute to the dipper phenomenon, including accretion-driven warps and "broken" discs caused by inclined (sub-)stellar or planetary companions.

Nonlinear interactions between phonon modes govern the behavior of vibrationally highly excited solids and molecules. Here, we demonstrate theoretically that optical cavities can be used to control the redistribution of energy from a highly excited coherent infrared-active phonon state into the other vibrational degrees of freedom of the system. The hybridization of the infrared-active phonon mode with the fundamental mode of the cavity induces a polaritonic splitting that we use to tune the nonlinear interactions with other vibrational modes in and out of resonance. We show that not only can the efficiency of the redistribution of energy be enhanced or decreased, but also the underlying scattering mechanisms may be changed. This work introduces the concept of cavity control to the field of nonlinear phononics, enabling nonequilibrium quantum optical engineering of new states of matter.

A common problem in cosmology is to integrate the product of two or more spherical Bessel functions (sBFs) with different configuration-space arguments against the power spectrum or its square, weighted by powers of wavenumber. Naively computing them scales as $N_{\rm g}^{p+1}$ with $p$ the number of configuration space arguments and $N_{\rm g}$ the grid size, and they cannot be done with Fast Fourier Transforms (FFTs). Here we show that by rewriting the sBFs as sums of products of sine and cosine and then using the product to sum identities, these integrals can then be performed using 1-D FFTs with $N_{\rm g} \log N_{\rm g}$ scaling. This "rotation" method has the potential to accelerate significantly a number of calculations in cosmology, such as perturbation theory predictions of loop integrals, higher order correlation functions, and analytic templates for correlation function covariance matrices. We implement this approach numerically both in a free-standing, publicly-available \textsc{Python} code and within the larger, publicly-available package \texttt{mcfit}. The rotation method evaluated with direct integrations already offers a factor of 6-10$\times$ speed-up over the naive approach in our test cases. Using FFTs, which the rotation method enables, then further improves this to a speed-up of $\sim$$1000-3000\times$ over the naive approach. The rotation method should be useful in light of upcoming large datasets such as DESI or LSST. In analysing these datasets recomputation of these integrals a substantial number of times, for instance to update perturbation theory predictions or covariance matrices as the input linear power spectrum is changed, will be one piece in a Monte Carlo Markov Chain cosmological parameter search: thus the overall savings from our method should be significant.

We propose Cormorant, a rotationally covariant neural network architecture for learning the behavior and properties of complex many-body physical systems. We apply these networks to molecular systems with two goals: learning atomic potential energy surfaces for use in Molecular Dynamics simulations, and learning ground state properties of molecules calculated by Density Functional Theory. Some of the key features of our network are that (a) each neuron explicitly corresponds to a subset of atoms; (b) the activation of each neuron is covariant to rotations, ensuring that overall the network is fully rotationally invariant. Furthermore, the non-linearity in our network is based upon tensor products and the Clebsch-Gordan decomposition, allowing the network to operate entirely in Fourier space. Cormorant significantly outperforms competing algorithms in learning molecular Potential Energy Surfaces from conformational geometries in the MD-17 dataset, and is competitive with other methods at learning geometric, energetic, electronic, and thermodynamic properties of molecules on the GDB-9 dataset.

Generative modeling with machine learning has provided a new perspective on the data-driven task of reconstructing quantum states from a set of qubit measurements. As increasingly large experimental quantum devices are built in laboratories, the question of how these machine learning techniques scale with the number of qubits is becoming crucial. We empirically study the scaling of restricted Boltzmann machines (RBMs) applied to reconstruct ground-state wavefunctions of the one-dimensional transverse-field Ising model from projective measurement data. We define a learning criterion via a threshold on the relative error in the energy estimator of the machine. With this criterion, we observe that the number of RBM weight parameters required for accurate representation of the ground state in the worst case - near criticality - scales quadratically with the number of qubits. By pruning small parameters of the trained model, we find that the number of weights can be significantly reduced while still retaining an accurate reconstruction. This provides evidence that over-parametrization of the RBM is required to facilitate the learning process.

We study the dynamics of charge-transfer insulators after a photo-excitation using the three-band Emery model which is relevant for the description of cuprate superconductors. We provide a detailed derivation of the nonequilibrium extension of the multi-band GW+EDMFT formalism and the corresponding downfolding procedure. The Peierls construction of the electron-light coupling is generalized to the multi-band case resulting in a gauge invariant combination of the Peierls intra-band acceleration and dipolar intra-band transitions. We apply the formalism to the study of momentum-dependent (inverse) photo-emission spectra and optical conductivities. The time-resolved spectral function shows a strong renormalization of the charge-transfer gap and a substantial broadening of some of the bands. While the upper Hubbard band exhibits a momentum-dependent broadening, an almost rigid band shift is observed for the ligand bands. The inverse photo-emission spectrum reveals that the inclusion of the non-local and inter-band charge fluctuations lead to a very fast relaxation of holes into the lower Hubbard band. Consistent with the changes in the spectral function, the optical conductivity shows a renormalization of the charge-transfer gap, which is proportional to the photo-doping. The details of the photo-induced changes strongly depend on the dipolar matrix elements, which calls for an ab-initio determination of these parameters.

A striking consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of a bijection between the local density and the ground-state many-body wave function. Here we study the problem of constructing approximations to the Hohenberg-Kohn map using a statistical learning approach. Using supervised deep learning with synthetic data, we show that this map can be accurately constructed for a chain of one-dimensional interacting spinless fermions, in different phases of this model including the charge ordered Mott insulator and metallic phases and the critical point separating them. However, we also find that the learning is less effective across quantum phase transitions, suggesting an intrinsic difficulty in efficiently learning non-smooth functional relations. We further study the problem of directly reconstructing complex observables from simple local density measurements, proposing a scheme amenable to statistical learning from experimental data.