Publications

We describe a formulation of the density matrix embedding theory at finite temperature. We present a generalization of the ground-state bath orbital construction that embeds a mean-field finite-temperature density matrix up to a given order in the Hamiltonian, or the Hamiltonian up to a given order in the density matrix. We assess the performance of the finite-temperature density matrix embedding on the one-dimensional Hubbard model both at half-filling and away from it, and the two-dimensional Hubbard model at half-filling, comparing to exact data where available, as well as results from finite-temperature density matrix renormalization group, dynamical mean-field theory, and dynamical cluster approximations. The accuracy of finite-temperature density matrix embedding appears comparable to that of the ground-state theory, with, at most, a modest increase in bath size, and competitive with that of cluster dynamical mean-field theory.

We derive analytic, closed-form solutions for the light curve of a planet transiting a star with a limb darkening profile which is a polynomial function of the stellar elevation, up to arbitrary integer order. We provide improved analytic expressions for the uniform, linear, and quadratic limb-darkened cases, as well as novel expressions for higher order integer powers of limb darkening. The formulae are crafted to be numerically stable over the expected range of usage. We additionally present analytic formulae for the partial derivatives of instantaneous flux with respect to the radius ratio, impact parameter, and limb darkening coefficients. These expressions are rapid to evaluate, and compare quite favorably in speed and accuracy to existing transit light curve codes. We also use these expressions to numerically compute the first partial derivatives of exposure-time averaged transit light curves with respect to all model parameters. An additional application is modeling eclipsing binary or eclipsing multiple star systems in cases where the stars may be treated as spherically symmetric. We provide code which implements these formulae in C++, Python, IDL, and Julia, with tests and examples of usage.

A large collaboration carefully benchmarks 20 first-principles many-body electronic structure methods on a test set of seven transition metal atoms and their ions and monoxides. Good agreement is attained between three systematically converged methods, resulting in experiment-free reference values. These reference values are used to assess the accuracy of modern emerging and scalable approaches to the many-electron problem. The most accurate methods obtain energies indistinguishable from experimental results, with the agreement mainly limited by the experimental uncertainties. A comparison between methods enables a unique perspective on calculations of many-body systems of electrons.

The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and interlayer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave state. We extract the Berezinskii-Kosterlitz-Thouless transition temperature from superfluid density and a finite-size scaling analysis of the correlation functions and explain our results in terms of an effective biexcitonic hard-core boson model.

We investigate the effect of nonlocal interactions on the photodoped Mott insulating state of the two-dimensional Hubbard model using a nonequilibrium generalization of the dynamical cluster approximation. In particular, we compare the situation where the excitonic states are lying within the continuum of doublon-holon excitations to a setup where the excitons appear within the Mott gap. In the first case, the creation of nearest-neighbor doublon-holon pairs by excitations across the Mott gap results in enhanced excitonic correlations, but these excitons quickly decay into uncorrelated doublons and holons. In the second case, photoexcitation results in long-lived excitonic states. While in a low-temperature equilibrium state, excitonic features are usually not evident in single-particle observables such as the photoemission spectrum, we show that the photoexcited nonequilibrium system can exhibit in-gap states associated with the excitons. The comparison with exact-diagonalization results for small clusters allows us to identify the signatures of the excitons in the photoemission spectrum.

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interactions between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a non-zero critical value pc of the hole doping p away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point pc is flanked by confining phases: a disordered Fermi liquid with carrier density 1+p for p>pc, and a metallic spin glass with carrier density p for p<pc. Additional evidence for the critical behavior is obtained from a large M analysis of a model which extends the SU(2) spin symmetry to SU(M). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.

Motivation
Breast cancer consists of multiple distinct tumor subtypes, and results from epigenetic and genetic aberrations that give rise to distinct transcriptional profiles. Despite previous efforts to understand transcriptional deregulation through transcription factor networks, the transcriptional mechanisms leading to subtypes of the disease remain poorly understood.

Results
We used a sophisticated computational search of thousands of expression datasets to define extended signatures of distinct breast cancer subtypes. Using ENCODE ChIP-seq data of surrogate cell lines and motif analysis we observed that these subtypes are determined by a distinct repertoire of lineage-specific transcription factors. Furthermore, specific pattern and abundance of copy number and DNA methylation changes at these TFs and targets, compared to other genes and to normal cells were observed. Overall, distinct transcriptional profiles are linked to genetic and epigenetic alterations at lineage-specific transcriptional regulators in breast cancer subtypes.

Terminal regions of the early Drosophila embryo are patterned by the highly conserved ERK cascade, giving rise to the nonsegmented terminal structures of the future larva. In less than an hour, this signaling event establishes several gene expression boundaries and sets in motion a sequence of elaborate morphogenetic events. Genetic studies of terminal patterning discovered signaling components and transcription factors that are involved in numerous developmental contexts and deregulated in human diseases. This review summarizes current understanding of signaling and morphogenesis during terminal patterning and discusses several open questions that can now be rigorously investigated using live imaging, omics, and optogenetic approaches. The anatomical simplicity of the terminal patterning system and its amenability to a broad range of increasingly sophisticated genetic perturbations will continue to make it a premier quantitative model for studying multiple aspects of tissue patterning by dynamically controlled cell signaling pathways.

The extracellular signal-regulated kinase (ERK) pathway is an essential component of developmental signaling in metazoans. Previous models of pathway activation suggested that dissociation of activated dually phosphorylated ERK (dpERK) from MAPK/ERK kinase (MEK), a kinase that phosphorylates ERK, and other cytoplasmic anchors, is sufficient for allowing ERK interactions with its substrates. Here, we provide evidence for an additional step controlling ERK’s access to substrates. Specifically, we demonstrate that interaction of ERK with its substrate Capicua (Cic) is controlled at the level of ERK phosphorylation, whereby Cic binds to dpERK much stronger than to unphosphorylated ERK, both in vitro and in vivo. Mathematical modeling suggests that the differential affinity of Cic for dpERK versus ERK is required for both down-regulation of Cic and stabilizing phosphorylated ERK. Preferential association of Cic with dpERK serves two functions: it prevents unproductive competition of Cic with unphosphorylated ERK and contributes to efficient signal propagation. We propose that high-affinity substrate binding increases the specificity and efficiency of signal transduction through the ERK pathway.

The coalescence of supermassive black holes (SMBHs) should generate the strongest sources of gravitational waves (GWs) in the Universe. However, the dynamics of their coalescence is the subject of much debate. In this study, we use a suite of N-body simulations to follow the merger of two nuclear star clusters (NSCs), each hosting a SMBH in their centre. We find that the presence of distinct star clusters around each SMBH has important consequences for the dynamical evolution of the SMBH binary: (i) The separation between the SMBHs decreases by a few orders of magnitude in the first few Myrs by the combined effects of dynamical friction and a drag force caused by tidally stripped stars. In fact, this is a significant speedup for equal mass ratio binaries, and becomes extreme for unequal mass ratios, e.g. 1:10 or 1:100, which traditional dynamical friction alone would not permit to bind. (ii) The subsequent binary hardening is driven by the gravitational slingshots between the SMBH binary and stars, and also depends on the mass ratio between the SMBHs. Thus, with this additional drag force, we find that all SMBHs in our suite coalesce within a Hubble time. Given that about 50% of Milky Way sized galaxies host NSCs, our results are encouraging for upcoming GW observations with the Laser Interferometer Space Antenna -- LISA -- which will detect SMBH coalescence in the 104−107M⊙ mass range.