Publications

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a nonconvex optimization problem. This article shows a remarkable result: despite the nonconvexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of nonconvex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber and Candes to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for nonconvex optimization and a novel way of exploiting nonconvexity for statistical inference.

A resonantly excited coherent phonon leads to a periodic oscillation of the atomic lattice in a crystal structure bringing the material into a non-equilibrium electronic configuration. Periodically oscillating quantum systems can be understood in terms of Floquet theory and we show these concepts can be applied to coherent lattice vibrations reflecting the underlying coupling mechanism between electrons and bosonic modes. This coupling leads to dressed quasi-particles imprinting specific signatures in the spectrum of the electronic structure. Taking graphene as a paradigmatic material we show how the phonon-dressed states display an intricate sideband structure revealing electron-phonon coupling and topological ordering. This work establishes that the recently demonstrated concept of light-induced non-equilibrium Floquet phases can also be applied when using coherent phonon modes for the dynamical control of material properties. The present results are generic for bosonic time-dependent perturbations and similar phenomena can be observed for plasmon, magnon or exciton driven materials.

Local spin fluctuations provide the glue for orbital-singlet spin-triplet pairing in the doped Mott insulating regime of multi-orbital Hubbard models. At large Hubbard repulsion U, the pairing susceptibility is nevertheless very low, because the pairing interaction cannot overcome the suppression of charge fluctuations. Using nonequilibrium dynamical mean field simulations of the two-orbital Hubbard model, we show that out of equilibrium the pairing susceptibility in this large-U regime can be strongly enhanced by creating a photo-induced population of the relevant charge states, and that this susceptibility correlates with the local spin susceptibility. Since a strong enhancement of the pairing requires a low kinetic energy of the charge carriers, the phenomenon is supported by the ultra-fast cooling of the photo-doped carriers through the creation of local spin excitations.

We extend the self-energy functional theory (SFT) to the case of interacting lattice bosons in the presence of symmetry breaking and quenched disorder. The self-energy functional we derive depends only on the self-energies of the disorder-averaged propagators, allowing for the construction of general non-perturbative approximations. Using a simple single-site reference system with only three variational parameters, we are able to reproduce numerically exact quantum Monte Carlo results in the Bose-Hubbard model with box disorder with high accuracy. Deep in the strongly-disordered weakly-interacting regime, the simple reference system employed is insufficient and no stationary solutions can be found within its restricted variational subspace. By systematically analyzing thermodynamical observables and the spectral function, we find that the strongly-interacting Bose glass is characterized by different regimes, depending on which local occupations are activated as a function of the disorder strength. We find that the particles delocalize into isolated superfluid lakes over a strongly localized background around maximally-occupied sites whenever these sites are particularly rare. Our results indicate that the transition from the Bose glass to the superfluid phase around unit filling at strong interactions is driven by the percolation of superfluid lakes which form around doubly occupied sites.

We consider a one-dimensional interacting spinless fermion model, which displays the well-known Luttinger liquid (LL) to charge density wave (CDW) transition as a function of the ratio between the strength of the interaction, U, and the hopping, J. We subject this system to a spatially uniform drive which is ramped up over a finite time interval and becomes time-periodic in the long time limit. We show that by using a density matrix renormalization group (DMRG) approach formulated for infinite system sizes, we can access the large-time limit even when the drive induces finite heating. When both the initial and long-time states are in the gapless (LL) phase, the final state has power law correlations for all ramp speeds. However, when the initial and final state are gapped (CDW phase), we find a pseudothermal state with an effective temperature that depends on the ramp rate, both for the Magnus regime in which the drive frequency is very large compared to other scales in the system and in the opposite limit where the drive frequency is less than the gap. Remarkably, quantum defects (instantons) appear when the drive tunes the system through the quantum critical point, in a realization of the Kibble-Zurek mechanism.

Many materials exhibit metal-insulator transitions that are driven by electron correlation effects but also involve structural changes. This paper uses density functional, dynamical mean field and Landau-theory methods to elucidate the interplay of electronic and structural energetics in Ca2RuO4. We find that the change in lattice energies across the metal-insulator transition is comparable to the change in electronic energies. Important consequences are the strongly first order nature of the transition, a sensitive dependence on pressure, and that imposition of geometrical constraints (for example via epitaxial growth on a substrate) can change the lattice energetics enough to eliminate the metal-insulator transition entirely. A comparison to recent data is presented.

Planets accompany most sun-like stars. The orbits of many are sufficiently close that they will be engulfed when their host stars ascend the giant branch. This Letter compares the power generated by orbital decay of an engulfed planet to the intrinsic stellar luminosity. Orbital decay power is generated by drag on the engulfed companion by the surrounding envelope. As stars ascend the giant branch their envelope density drops and so does the power injected through orbital decay, scaling approximately as Ldecay∝R−9/2∗. Their luminosity, however, increases along the giant branch. These opposed scalings indicate a crossing, where Ldecay=L∗. We consider the engulfment of planets along isochrones in the Hertzsprung-Russell (H-R) diagram. We find that the conditions for such a crossing occur around L∗≈102~L⊙ (or a≈0.1~au) for Jovian planetary companions. The consumption of closer-in giant planets, such as hot Jupiters, leads to Ldecay≫L∗, while more distant planets such as warm Jupiters, a≈0.5~au, lead to minor perturbations of their host stars with Ldecay≪L∗. Our results map out the parameter space along the giant branch in the H-R Diagram where interaction with planetary companions leads to significant energetic disturbance of host stars.

We have used a combination of ultrafast coherent phonon spectroscopy, ultrafast thermometry, and time-dependent Landau theory to study the inversion symmetry breaking phase transition at Tc=200 K in the strongly spin-orbit coupled correlated metal Cd2Re2O7. We establish that the structural distortion at Tc is a secondary effect through the absence of any softening of its associated phonon mode, which supports a purely electronically driven mechanism. However, the phonon lifetime exhibits an anomalously strong temperature dependence that decreases linearly to zero near Tc. We show that this behavior naturally explains the spurious appearance of phonon softening in previous Raman spectroscopy experiments and should be a prevalent feature of correlated electron systems with linearly coupled order parameters.

We study numerically the expansion dynamics of an initially confined quantum wave packet in the presence of a disordered potential and a uniform bias force. For white-noise disorder, we find that the wave packet develops asymmetric algebraic tails for any ratio of the force to the disorder strength. The exponent of the algebraic tails decays smoothly with that ratio and no evidence of a critical behavior on the wave density profile is found. Algebraic localization features a series of critical values of the force-to-disorder strength where the m-th position moment of the wave packet diverges. Below the critical value for the m-th moment, we find fair agreement between the asymptotic long-time value of the m-th moment and the predictions of diagrammatic calculations. Above it, we find that the m-th moment grows algebraically in time. For correlated disorder, we find evidence of systematic delocalization, irrespective to the model of disorder. More precisely, we find a two-step dynamics, where both the center-of-mass position and the width of the wave packet show transient localization, similar to the white-noise case, at short time and delocalization at sufficiently long time. This correlation-induced delocalization is interpreted as due to the decrease of the effective de Broglie wavelength, which lowers the effective strength of the disorder in the presence of finite-range correlations.

Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems. In this paper, we fill this gap by showing that proximal methods provide an efficient framework to model and solve problems involving perspective functions. We study the construction of the proximity operator of a perspective function under general assumptions and present important instances in which the proximity operator can be computed explicitly or via straightforward numerical operations. These results constitute central building blocks in the design of proximal optimization algorithms. We showcase the versatility of the framework by designing novel proximal algorithms for state-of-the-art regression and variable selection schemes in high-dimensional statistics.