Publications

We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an anti-ferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods, established the stripe order as the ground state near 1/8 doping at strong interactions. In this work, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes in the pure Hubbard model.

We perform large-scale, numerically exact calculations on the two-dimensional interacting Fermi gas with a contact attraction. Reaching much larger lattice sizes and lower temperatures than previously possible, we determine systematically the finite-temperature phase diagram of the Berezinskii-Kosterlitz-Thouless (BKT) transitions for interaction strengths ranging from BCS to crossover to BEC regimes. The evolutions of the pairing wavefunctions and the fermion and Cooper pair momentum distributions with temperature are accurately characterized. In the crossover regime, we find that the contact has a non-monotonic temperature dependence, first increasing as temperature is lowered, and then showing a slight decline below the BKT transition temperature to approach the ground-state value from above.

Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly 500 atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between interaction and superfluidity in an exotic phase of matter.

The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas-phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multi-determinant trial wavefunctions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies to experimental results. We find that ph-AFQMC yields mean averaged errors (MAE) of 1.69±1.02 kcal/mol for the adiabatic energies and 2.85±1.13 kcal/mol for the vertical energies. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields MAE’s of 3.62 to 6.98 and 3.31 to 9.88 kcal/mol, as well as a localized coupled cluster approach (DLPNO-CCSD(T0)), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T0) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and find much higher MAE’s, ranging from 4.56 kcal/mol to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T0). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.

Using the time-dependent Ginzburg Landau equations we study vortex motion driven by an applied current in two dimensional superconductors in the presence of a physical boundary. At smaller sourced currents the vortex lattice moves as a whole, with each vortex moving at the same velocity. At larger sourced current, vortex motion is organized into channels, with vortices in channels nearer to the sample edges moving faster than those farther away from sample edges, opposite to the Poiseuille flow of basic hydrodynamics where the velocity is lowest at the boundaries. At intermediate currents, a stick-slip motion of the vortex lattice occurs in which vortices in the channel at the boundary break free from the Abrikosov lattice, accelerate, move past their neighbors and then slow down and reattach to the vortex lattice at which point the stick-slip process starts over. These effects could be observed experimentally, e.g. using fast scanning microscopy techniques.

Nonlinear optics in topological semimetals is a burgeoning field of research with an expanding list of new materials but limited choice of probes. We devised, modeled, and implemented an approach for investigating nonlinear optics at the nanoscale with a metallic tip. Far-field nonlinear optics are diffraction-limited and probe the in-plane response only. Our tip-based approach circumvents the diffraction limit and provides strong field enhancement for both in-plane and out-of-plane fields. We therefore gain access to complete nonlinear tensors including components not attainable before. One immediate application of our approach is the separation of surface state and bulk nonlinear responses in Weyl semimetals. Applying near-field probes to topological semimetals constitutes a new paradigm of research on nanoscale nonlinearity. Chiral Weyl fermions with linear energy-momentum dispersion in the bulk accompanied by Fermi-arc states on the surfaces prompt a host of enticing optical effects. While new Weyl semimetal materials keep emerging, the available optical probes are limited. In particular, isolating bulk and surface electrodynamics in Weyl conductors remains a challenge. We devised an approach to the problem based on near-field photocurrent imaging at the nanoscale and applied this technique to a prototypical Weyl semimetal TaIrTe4. As a first step, we visualized nano-photocurrent patterns in real space and demonstrated their connection to bulk nonlinear conductivity tensors through extensive modeling augmented with density functional theory calculations. Notably, our nanoscale probe gives access to not only the in-plane but also the out-of-plane electric fields so that it is feasible to interrogate all allowed nonlinear tensors including those that remained dormant in conventional far-field optics. Surface- and bulk-related nonlinear contributions are distinguished through their “symmetry fingerprints” in the photocurrent maps. Robust photocurrents also appear at mirror-symmetry breaking edges of TaIrTe4 single crystals that we assign to nonlinear conductivity tensors forbidden in the bulk. Nano-photocurrent spectroscopy at the boundary reveals a strong resonance structure absent in the interior of the sample, providing evidence for elusive surface states.

Deep neural networks have provided state-of-the-art solutions for problems such as image denoising, which implicitly rely on a prior probability model of natural images. Two recent lines of work – Denoising Score Matching and Plug-and-Play – propose methodologies for drawing samples from this implicit prior and using it to solve inverse problems, respectively. Here, we develop a parsimonious and robust generalization of these ideas. We rely on a classic statistical result that shows the least-squares solution for removing additive Gaussian noise can be written directly in terms of the gradient of the log of the noisy signal density. We use this to derive a stochastic coarse-to-fine gradient ascent procedure for drawing high-probability samples from the implicit prior embedded within a CNN trained to perform blind denoising. A generalization of this algorithm to constrained sampling provides a method for using the implicit prior to solve any deterministic linear inverse problem, with no additional training, thus extending the power of supervised learning for denoising to a much broader set of problems. The algorithm relies on minimal assumptions and exhibits robust convergence over a wide range of parameter choices. To demonstrate the generality of our method, we use it to obtain state-of-the-art levels of unsupervised performance for deblurring, super-resolution, and compressive sensing.

Polaritonic chemistry has become a rapidly developing field within the last few years. A multitude of experimental observations suggest that chemical properties can be fundamentally altered and novel physical states appear when matter is strongly coupled to resonant cavity modes, i.e. when hybrid light-matter states emerge. Up until now, theoretical approaches to explain and predict these observations were either limited to phenomenological quantum optical models, suited to describe collective polaritonic effects, or alternatively to ab initio approaches for small system sizes. The later methods were particularly controversial since collective effects could not be explicitly included due to the intrinsically low particle numbers, which are computationally accessible. Here, we demonstrate for a nitrogen dimer chain of variable size that any impurity present in a collectively coupled chemical ensemble (e.g. temperature fluctuations or reaction process) induces local modifications in the polaritonic system. From this we deduce that a novel dark state is formed, whose local chemical properties are modified considerably at the impurity due to the collectively coupled environment. Our simulations unify theoretical predictions from quantum optical models (e.g. formation of collective dark states and different polaritonic branches) with the single molecule quantum chemical perspective, which relies on the (quantized) redistribution of local charges. Moreover, our findings suggest that the recently developed QEDFT method is suitable to access these locally scaling polaritonic effects and it is a useful tool to better understand recent experimental results and to even design novel experimental approaches. All of which paves the way for many novel discoveries and applications in polaritonic chemistry.

The one-point probability distribution function (PDF) is a powerful summary statistic for non-Gaussian cosmological fields, such as the weak lensing (WL) convergence reconstructed from galaxy shapes or cosmic microwave background (CMB) maps. Thus far, no analytic model has been developed that successfully describes the high-convergence tail of the WL convergence PDF for small smoothing scales from first principles. Here, we present a halo-model formalism to compute the WL convergence PDF, building upon our previous results for the thermal Sunyaev-Zel'dovich field. Furthermore, we extend our formalism to analytically compute the covariance matrix of the convergence PDF. Comparisons to numerical simulations generally confirm the validity of our formalism in the non-Gaussian, positive tail of the WL convergence PDF, but also reveal the convergence PDF's strong sensitivity to small-scale systematic effects in the simulations (e.g., due to finite resolution). Finally, we present a simple Fisher forecast for a Rubin-Observatory-like survey, based on our new analytic model. Considering the {As,Ωm,Σmν} parameter space and assuming a Planck CMB prior on As only, we forecast a marginalized constraint σ(Σmν)≈0.08 eV from the WL convergence PDF alone, even after marginalizing over parameters describing the halo concentration-mass relation. This error bar on the neutrino mass sum is comparable to the minimum value allowed in the normal hierarchy, illustrating the strong constraining power of the WL convergence PDF. We make our code publicly available \href{https://github.com/leanderthiele/hmpdf}{at this https URL}.

The search for primordial gravitational waves in the Cosmic Microwave Background (CMB) will soon be limited by our ability to remove the lensing contamination to B-mode polarization. The often-used quadratic estimator for lensing is known to be suboptimal for surveys that are currently operating and will continue to become less and less efficient as instrumental noise decreases. While foregrounds can in principle be mitigated by observing in more frequency bands, progress in delensing hinges entirely on algorithmic advances. We demonstrate here a new inference method that solves this problem by sampling the exact Bayesian posterior of any desired cosmological parameters, of the gravitational lensing potential, and of the delensed CMB maps, given lensed temperature and polarization data. We validate the method using simulated CMB data with non-white noise and masking on up to 650\,deg2 patches of sky. A unique strength of this approach is the ability to jointly estimate cosmological parameters which control both the primordial CMB and the lensing potential, which we demonstrate here for the first time by sampling both the tensor-to-scalar ratio, r, and the amplitude of the lensing potential, Aϕ. The method allows us to perform the most precise check to-date of several important approximations underlying CMB-S4 r forecasting, and we confirm these yield the correct expected uncertainty on r to better than 10%.