Abstract: Fractional Chern insulators (FCIs) in moiré materials present a unique platform for exploring strongly correlated topological phases beyond the paradigm of ideal quantum geometry. While analytical approaches to FCIs and fractional quantum Hall states (FQHS) often rely on idealized Bloch wavefunctions, realistic moiré models lack direct tunability of quantum metric and Berry curvature, limiting theoretical and numerical exploration. Here, we introduce an unsupervised machine learning framework to model interacting Hamiltonians directly through the distribution of single-particle form factors. Using a variational autoencoder (VAE), we show that unsupervised learning can not only distinguish FCI and non-FCI states, but also generate new form factors with distinct topological character, not present in the training set. This latent space enables the generation and interpolation of form factors for topological flatbands with Chern number ∣C∣ = 1, enabling the discovery of unobserved many-body states such as charge density waves. Principal component analysis (PCA) further reveals that the dominant patterns in the form factors—reflecting correlations across the Brillouin zone—can be decomposed into components with approximately quantized Chern numbers, providing new insights into the global and topological structure of quantum geometry. Our results highlight the ability of machine learning to generalize and model topological quantum systems, paving the way for the inverse design of form factors with tailored quantum geometry and many-body phases in flatband materials.
We consider the problem of community detection or clustering in the labeled Stochastic Block Model (LSBM) with a finite number $K$ of clusters of sizes linearly growing with the global population of items $n$. Every pair of items is labeled independently at random, and label $\ell$ appears with probability $p(i,j,\ell)$ between two items in clusters indexed by $i$ and $j$, respectively. The objective is to reconstruct the clusters from the observation of these random labels. Clustering under the SBM and their extensions has attracted much attention recently. Most existing work aimed at characterizing the set of parameters such that it is possible to infer clusters either positively correlated with the true clusters, or with a vanishing proportion of misclassified items, or exactly matching the true clusters. We find the set of parameters such that there exists a clustering algorithm with at most $s$ misclassified items in average under the general LSBM and for any $s=o(n)$, which solves one open problem raised in \cite{abbe2015community}. We further develop an algorithm, based on simple spectral methods, that achieves this fundamental performance limit within $O(n \mbox{polylog}(n))$ computations and without the a-priori knowledge of the model parameters.
We perform a set of high-fidelity simulations of geochemical reactions within three-dimensional discrete fracture networks (DFN) and use various machine learning techniques to determine the primary factors controlling mineral dissolution. The DFN are partially filled with quartz that gradually dissolves until quasi-steady state conditions are reached. At this point, we measure the quartz remaining in each fracture within the domain as our primary quantity of interest. We observe that a primary sub-network of fractures exists, where the quartz has been fully dissolved out. This reduction in resistance to flow leads to increased flow channelization and reduced solute travel times. However, depending on the DFN topology and the rate of dissolution, we observe substantial variability in the volume of quartz remaining within fractures outside of the primary subnetwork. This variability indicates an interplay between the fracture network structure and geochemical reactions. We characterize the features controlling these processes by developing a machine learning framework to extract their relevant impact. Specifically, we use a combination of high-fidelity simulations with a graph-based approach to study geochemical reactive transport in a complex fracture network to determine the key features that control dissolution. We consider topological, geometric and hydrological features of the fracture network to predict the remaining quartz in quasi-steady state. We found that the dissolution reaction rate constant of quartz and the distance to the primary sub-network in the fracture network are the two most important features controlling the amount of quartz remaining. This study is a first step towards characterizing the parameters that control carbon mineralization using an approach with integrates computational physics and machine learning.
The synthesis of novel carbon nanostructures with unique topologies expands the landscape of organic molecules, introducing new chemical properties and potential applications. Carbon nanorings, composed of cyclic paraphenylene (CPP) chains, serve as a versatile scaffold for designing materials with unique molecular architectures that impact their optical properties and photoinduced dynamics. These new topologies alter the balance between competing π-conjugation effects, high bending strain energies, and steric hindrances imposed by the rearrangement of their cyclic structures. Here, we explore the photoinduced dynamics of the all-benzene trefoil knot using nonadiabatic excited-state molecular dynamics. We show how its absorption spectra can be modeled by a particle in a box constrained to the trefoil knot geometry, and we analyze the internal conversion process following photoexcitation. Our findings reveal an exciton intraring migration governed by the winding of the paraphenylene chain, ultimately leading to exciton self-trapping at specific high curvature regions of the knot. This behavior contrasts with the nondeterministic exciton self-trapping in the corresponding CPP, where localization occurs randomly across different phenylene units. Our results highlight the ability of molecular knots to control exciton dynamics through curvature, tension, and planarization effects, positioning these materials as promising candidates for future technological applications. This ability to precisely manipulate optical and electronic characteristics is essential for developing more efficient and versatile devices.
International migrants, especially those belonging to key populations, face a considerable HIV burden. However, continuity of HIV care for this group is often challenged along the migration route. We assess the available evidence on the existing interventions that aim to strengthen community and health systems to ensure the continuity of HIV care for international migrants. We did a systematic search of PubMed for publications from 1989 until 2023 focused on different stages of the HIV care continuum regardless of the geographical region. The literature was reviewed with a thematic approach. Globally, legal regulations can restrict access to HIV care and fuel fear of deportation among undocumented migrants. The intersection of HIV-related and migration-related stigma creates further challenges for uninterrupted access to HIV care along the migration route, with negative clinical and public health consequences. Different potential interventions were identified including: provision of HIV care regardless of migration status; utilisation of mobile health, mobile units, and community-led initiatives to bring HIV care to migrants; and utilisation of participatory and co-creation methods to develop tailored and sustainable HIV-related interventions with migrant communities. Improving access to the continuity of care for migrants requires a shift towards intersectional policies rooted in co-creation approaches to address the underlying multiple and mutually reinforcing inequalities.
