Persistent homology of quantum entanglement

Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix product states for local and gapped Hamiltonians. We study the structure of entanglement entropy using persistent homology, a relatively new method from the field of topological data analysis. The inverse quantum mutual information between pairs of sites is used as a distance metric to form a filtered simplicial complex. Both ground states and excited states of common spin models are analyzed as an example. Furthermore, the effect of homology with different coefficients and boundary conditions is also explored. Beyond these basic examples, we also discuss the promising future applications of this modern computational approach, including its connection to the question of how spacetime could emerge from entanglement.Comment: 14 pages, 12 figure

Mass fluctuations and absorption rates in Dirac materials sensors

We study the mass fluctuations in gapped Dirac materials by treating the mass-term as both a continuous and discrete random variable. Gapped Dirac materials were proposed to be used as materials for Dark matter sensors. One thus would need to estimate the role of disorder and fluctuations on the interband absorption of dark matter. We find that both continuous and discrete fluctuations across the sample introduce tails (e.g. Lifshitz tails) in the density of states and the interband absorption rate. We estimate the strength of the gap filling and discuss implications of these fluctuations on the performance as sensors for Dark matter detection. The approach used in this work provides a basic framework to model the disorder by any arbitrary mechanism on the interband absorption of Dirac material sensors.Comment: 7 pages, 5 figure

Band gap prediction for large organic crystal structures with machine learning

Machine-learning models are capable of capturing the structure-property relationship from a dataset of computationally demanding ab initio calculations. Over the past two years, the Organic Materials Database (OMDB) has hosted a growing number of calculated electronic properties of previously synthesized organic crystal structures. The complexity of the organic crystals contained within the OMDB, which have on average 82 atoms per unit cell, makes this database a challenging platform for machine learning applications. In this paper, the focus is on predicting the band gap which represents one of the basic properties of a crystalline materials. With this aim, a consistent dataset of 12 500 crystal structures and their corresponding DFT band gap are released, freely available for download at https://omdb.mathub.io/dataset. An ensemble of two state-of-the-art models reach a mean absolute error (MAE) of 0.388 eV, which corresponds to a percentage error of 13% for an average band gap of 3.05 eV. Finally, the trained models are employed to predict the band gap for 260 092 materials contained within the Crystallography Open Database (COD) and made available online so that the predictions can be obtained for any arbitrary crystal structure uploaded by a user.Comment: 10 pages, 6 figure

Finding hidden order in spin models with persistent homology

Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models, including hidden order such as spin nematic ordering and spin liquids. By converting a small number of spin configurations to barcodes we obtain a descriptive picture of configuration space. Using dimensionality reduction to reduce the barcode space to color space leads to a visualization of the phase diagram.Comment: 8 pages, 6 figure

Online Search Tool for Graphical Patterns in Electronic Band Structures

We present an online graphical pattern search tool for electronic band structure data contained within the Organic Materials Database (OMDB) available at https://omdb.diracmaterials.org/search/pattern. The tool is capable of finding user-specified graphical patterns in the collection of thousands of band structures from high-throughput ab initio calculations in the online regime. Using this tool, it only takes a few seconds to find an arbitrary graphical pattern within the ten electronic bands near the Fermi level for 26,739 organic crystals. The tool can be used to find realizations of functional materials characterized by a specific pattern in their electronic structure, for example, Dirac materials, characterized by a linear crossing of bands; topological insulators, characterized by a "Mexican hat" pattern or an effectively free electron gas, characterized by a parabolic dispersion. The source code of the developed tool is freely available at https://github.com/OrganicMaterialsDatabase/EBS-search and can be transferred to any other electronic band structure database. The approach allows for an automatic online analysis of a large collection of band structures where the amount of data makes its manual inspection impracticable.Comment: 8 pages, 8 figure

Materials Informatics for Dark Matter Detection

Dark Matter particles are commonly assumed to be weakly interacting massive particles (WIMPs) with a mass in the GeV to TeV range. However, recent interest has shifted towards lighter WIMPs, which are more difficult to probe experimentally. A detection of sub-GeV WIMPs would require the use of small gap materials in sensors. Using recent estimates of the WIMP mass, we identify the relevant target space towards small gap materials (100-10 meV). Dirac Materials, a class of small- or zero-gap materials, emerge as natural candidates for sensors for Dark Matter detection. We propose the use of informatics tools to rapidly assay materials band structures to search for small gap semiconductors and semimetals, rather than focusing on a few preselected compounds. As a specific example of the proposed strategy, we use the organic materials database (omdb.diracmaterials.org) to identify organic candidates for sensors: the narrow band gap semiconductors BNQ-TTF and DEBTTT with gaps of 40 and 38 meV, and the Dirac-line semimetal (BEDT-TTF)$\cdot$Br which exhibits a tiny gap of $\approx$ 50 meV when spin-orbit coupling is included. We outline a novel and powerful approach to search for dark matter detection sensor materials by means of a rapid assay of materials using informatics tools.Comment: 5 pages, 3 figure

Homology and machine learning for materials informatics

Materials informatics is the field of study where materials science is combined with modern data science. This data-driven approach is powered by the growing availability of computational power and storage capability. The development and application of these methods accelerates materials science and represents an effective way to study and model material properties. This thesis is a compilation of theoretical and computational works that can be divided into three key areas: materials databases, machine learning for materials, and homology for materials. Machine learning and data mining rely on the availability of materials databases to test methods and models. The Organic Materials Database (OMDB), for example, contains a large number of organic crystals and their corresponding electronic structures. The electronic properties of the organic crystals are computed using atomic scale materials modelling, which is computationally expensive because organic crystals typically contain many atoms in the unit cell. However, the resulting data can be used in a variety of materials informatics applications. We demonstrate data mining for dark matter sensors as an example application. Accurate machine learning models can capture the structure-property relationship of materials and accelerate the discovery of new materials with desired properties. This is explored by investigating the properties of the organic crystals in the OMDB. For example, we employ supervised learning on the electronic band gap, an important material property for technological applications. Unsupervised learning is used to construct a dimensionality-reduced chemical space that reveals interesting clusters of materials. Finally, persistent homology is a relatively new method from the field of algebraic topology that studies the shapes that are present in data at different length scales. In this thesis, the method is used to study magnetic materials and their phase transitions. More specifically, in the case of classical models, we use persistent homology to detect the phase transition directly from sampled spin configurations. For quantum spin models, the shapes in the entanglement structure are captured and a sudden change reveals a quantum phase transition. In summary, these three topics provide an overview on how to study material properties with modern data science methods. The tools can be used in combination with the traditional methods in materials science and accelerate materials design.Materialinformatik är ett forskningsområde där materialvetenskap kombineras med modern datavetenskap. Detta datadrivna tillvägagångssätt drivs av den växande tillgängligheten av beräkningskraft och lagringskapacitet. Utvecklingen och tillämpningen av dessa metoder accelererar materialvetenskapen och utgör ett effektivt sätt att studera och modellera materialegenskaper. Denna avhandling är en sammanställning av teoretiska och beräkningstekniska arbeten som kan delas in i tre nyckelområden: materialdatabaser, maskininlärning för material och homologi för material. Maskininlärning och datautvinning är beroende av tillgången på materialdatabaser för att testa metoder och modeller. Organic Materials Database (OMDB) innehåller data för kristallin struktur och elektroniska egenskaper för ett stort antal organiska kristaller. De elektroniska egenskaperna hos de organiska kristallerna beräknas med hjälp av materialmodellering i atomskala, vilket är beräkningsmässigt dyrt då organiska kristaller vanligtvis innehåller många atomer i enhetscellen. Emellertid kan den resulterande datan användas i en mängd olika materialinformatikapplikationer. Vi demonstrerar datautvinning för att söka material till sensor för mörk materia som ett exempel på applikation. Maskininlärningsmetoder kan fånga förhållanden mellan struktur och egenskap hos material, och därmed påskynda upptäckten av nya material med önskade egenskaper. Detta utforskas genom att undersöka egenskaperna hos de organiska kristallerna i OMDB. Till exempel använder vi övervakat lärande på elektroniska bandgap, en viktig materiell egenskap för tekniska tillämpningar. Oövervakat lärande används för att konstruera en dimensionsreducerad kemisk rymd som avslöjar intressanta kluster av material. Slutligen är ihållande homologi en relativt ny metod från området algebraisk topologi som studerar de former som finns i data i olika längdskalor. I denna avhandling används metoden för att studera magnetiska material och deras fasövergångar. Mer specifikt, när det gäller klassiska modeller, använder vi ihållande homologi för att detektera fasövergången direkt från samplade spin-konfigurationer. För kvantspinnmodeller fångas faserna i strukturen hos den kvantmekaniska sammanflätningen och en plötslig förändring avslöjar en kvantfasövergång. Sammantaget utgör dessa tre ämnen ett bra exempel på hur materialegenskaper kan studeras med moderna datavetenskapliga metoder. Verktygen kan användas i kombination med traditionella metoder inom materialvetenskap och påskynda materialdesign.QC 230227</p

Quantification of epicardial adipose tissue in patients undergoing hybrid ablation for atrial fibrillation

OBJECTIVES: Epicardial adipose tissue volume (EAT-V) has been linked to atrial fibrillation (AF) recurrences after catheter ablation. We retrospectively studied the association between atrial EAT-V and outcome after hybrid AF ablation (epicardial surgical and endocardial catheter ablation). METHODS: On preoperative cardiac computed tomography angiography scans, the left atrium and right atrium were manually delineated using the open source Image J. With custom-made automated software, the number of pixels in the regions of interest on each slice was calculated. On the basis of the Hounsfield units, pixel size and slice thickness, EAT-V was computed and normalized in relation to the body surface area (BSA) and the myocardial tissue volume. RESULTS: Eighty-five patients were included. Left atrial and right atrial EAT-V normalized to BSA were not significantly different between paroxysmal and persistent AF [0.84 (0.51-1.50) vs 0.81 (0.57-1.18), 1.74 (1.02-2.56) vs 1.55 (1.26-2.18), all P = 0.9], neither between the acute conduction block and no acute conduction block in the epicardial box lesion [0.92 (0.55-1.39) vs 0.72 (0.55-1.24), P = 0.5, right atrium not applicable], nor between the sinus rhythm and arrhythmia recurrence after 12 months [0.88 (0.55-1.48) vs 0.63 (0.47-1.10), 1.61 (1.11-2.50) vs 1.55 (1.20-2.20), all P > 0.1]. Left atrial EAT-V normalized to myocardial tissue volume was not different between the groups. CONCLUSIONS: This study could neither confirm that EAT-V was predictive of recurrence of supraventricular arrhythmias in patients undergoing a hybrid AF ablation, nor that EAT-V was different between patients with paroxysmal AF and persistent and long-standing persistent AF. This suggests that EAT-V might not affect the outcome in surgical ablation procedures and therefore should not influence preoperative or intraoperative decision-making

Postoperative atrial fibrillation and atrial epicardial fat:Is there a link?

BACKGROUND: Atrial Epicardial Adipose Tissue (EAT) is presumably involved in the pathogenesis of atrial fibrillation (AF). The transient nature of postoperative AF (POAF) suggests that surgery-induced triggers provoke an unmasking of a pre-existent AF substrate. The aim is to investigate the association between the volume of EAT and the occurrence of POAF. We hypothesise that the likelihood of developing POAF is higher in patients with high compared to low left atrial (LA) EAT volumes. METHODS: Quantification of LA EAT based on the Hounsfield Units using custom made software was performed on pre-operative coronary computed tomography angiography scans of patients who underwent cardiac surgery between 2009 and 2019. Patients with mitral valve disease were excluded. RESULTS: A total of 83 patients were included in this study (CABG = 34, aortic valve = 33, aorta ascendens n = 7, combination n = 9), of which 43 patients developed POAF. The EAT percentage in the LA wall nor indexed EAT volumes differed between patients with POAF and with sinus rhythm (all P > 0.05). In multivariable analysis, age and LA volume index (LAVI) were the only independent predictors for early POAF (OR: 1.076 and 1.056, respectively). CONCLUSIONS: As expected, advanced age and LAVI were independent predictors of POAF. However, the amount of local EAT was not associated with the occurrence of AF after cardiac surgery. This suggests that the role of EAT in POAF is rather limited, or that the association of EAT in the early phase of POAF is obscured by the dominance of surgical-induced triggers