Efficient Learning of a One-dimensional Density Functional Theory

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In addition, the computational result---energy and charge density distribution of the ground state---is useful for electronic properties of solids mostly when reduced to a band structure interpretation based on the Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can help to free density functional theory from these limitations. We study a theory of spinless fermions on a one-dimensional lattice. The density functional is implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions. At no point do we require a band structure interpretation. The training data, obtained via exact diagonalization, feeds into a learning scheme inspired by active learning, which minimizes the computational costs for data generation. We show that the network results are of high quantitative accuracy and, despite learning on random potentials, capture both symmetry-breaking and topological phase transitions correctly.Comment: 5 pages, 3 figures; 4+ pages appendi

The Mourides of Senegal: A Gospel of Work, Solidarity & God

Islamic religiosity is a phrase that often conjures up images of patriarchal societies, conservative, bordering repressive moral tenents, angry demonstrations, even violence. But the Mourides are different

Four- and twelve-band low-energy symmetric Hamiltonians and Hubbard parameters for twisted bilayer graphene using ab-initio input

A computationally efficient workflow for obtaining low-energy tight-binding Hamiltonians for twisted bilayer graphene, obeying both crystal and time-reversal symmetries, is presented in this work. The Hamiltonians at the first magic angle are generated using the Slater-Koster approach with parameters obtained by a fit to ab-initio data at larger angles. Low-energy symmetric four-band and twelve-band Hamiltonians are constructed using the Wannier90 software. The advantage of our scheme is that the low-energy Hamiltonians are purely real and are obtained with the maximum-localization procedure to reduce the spread of the basis functions. Finally, we compute extended Hubbard parameters for both models within the constrained random phase approximation (cRPA) for screening, which again respect the symmetries. The relevant data and results of this work are freely available via an online repository. The workflow is straightforwardly transferable to other twisted multi-layer materials.Comment: 14 pages, 8 figure

Pairing Obstructions in Topological Superconductors

The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor, we show that the wave function of an individual Cooper pair decays exponentially with separation in the trivial phase and polynomially in the topological phase. For the position-space Majorana representation, we show that the topological phase is characterized by a nonzero Majorana polarization, which captures an irremovable and quantized separation of Majorana Wannier centers from the atomic positions. We apply our results to diagnose second-order topological superconducting phases in two dimensions. Our work establishes a vantage point for the generalization of Topological Quantum Chemistry to superconductivity.Comment: 6 pages, 3 figures, accepted manuscript, supplement include

Sotauutisoinnin rintamalinjat : Miten suomalaistoimittajat kohtasivat Yhdysvaltain armeijan uutisohjailun Persianlahden ja Irakin sodissa

Only abstract. Paper copies of master’s theses are listed in the Helka database (http://www.helsinki.fi/helka). Electronic copies of master’s theses are either available as open access or only on thesis terminals in the Helsinki University Library.Vain tiivistelmä. Sidottujen gradujen saatavuuden voit tarkistaa Helka-tietokannasta (http://www.helsinki.fi/helka). Digitaaliset gradut voivat olla luettavissa avoimesti verkossa tai rajoitetusti kirjaston opinnäytekioskeilla.Endast sammandrag. Inbundna avhandlingar kan sökas i Helka-databasen (http://www.helsinki.fi/helka). Elektroniska kopior av avhandlingar finns antingen öppet på nätet eller endast tillgängliga i bibliotekets avhandlingsterminaler.Pro gradu -tutkielmassa tarkastellaan Persianlahden ja Irakin sodissa esiintynyttä uutisohjailua – kuinka suomalaistoimittajat kohtasivat ja jälkikäteen arvioivat näitä Yhdysvaltain armeijan vaikutusyrityksiä. Persianlahden sodassa journalistit kamppailivat informaatiosta tarkoin kontrolloiduissa uutispooleissa kaukana varsinaisilta taistelukentiltä. Irakin sodassa taas liittouman joukkojen mukana matkasi satoja kansainvälisiä toimittajia aina eturintamaan saakka. Molemmissa konflikteissa Yhdysvaltain puolustushallinto panosti merkittäviä rahasummia julkisuuden hallintaan: tiedon kontrollointi, levittäminen ja jopa väärentäminen olivat yksi sodankäynnin muoto. Pro gradussa on haluttu selvittää, millä keinoin Yhdysvaltain armeija pyrki vaikuttamaan joukkoviestimien välittämiin uutisiin. Lisäksi on etsitty vastausta siihen, miten sotien välillä muuttunut tiedotuskäytäntö vaikutti uutisointiin ja rajasiko se toimittajien mahdollisuutta tietojen tarkistamiseen. Samalla nousevat esiin myös median muuttunut rooli, sähköistyneen tiedonvälityksen pyrkimys reaaliaikaiseen uutisointiin ja eri mediatalojen väliset taloudelliset sidonnaisuudet. Vaikka sodissa esiintynyt uutisohjailu kohdistui kansainväliseen mediaan kokonaisuudessaan, rajauksena on käytetty nimenomaan kotimaisia tiedotusvälineitä. Tutkimusongelmaa lähestytään kahdella rinnakkaisella tutkimusmetodilla. Sotauutisointia suorittaneiden toimittajien mielipiteitä on selvitetty teemahaastattelulla, jonka jäsentelyyn on käytetty apuna Pamela J. Shoemakerin ja Stephen D. Reesen joukkoviestinnän mallia. Työn toinen tutkimusosuus muodostuu valittujen sotapäivien media-analyysistä. Työssä ei kuitenkaan pyritä mittaamaan Yhdysvaltain armeijan tosiasiallista vaikutusta sotauutisointiin, tai nostamaan esiin yksittäisiä virheelliseksi osoittautuneita mediatallenteita. Työn tutkimustulokset osoittavat Yhdysvaltain armeijan pyrkineen ohjailemaan sotauutisointia molemmissa konflikteissa ja nämä vaikutusyritykset kohdistuivat kiistattomasti myös suomalaisiin viestimiin. Näistä ohjailupyrkimyksistä huolimatta suomalaiset journalistit uskovat tuottamansa sotauutisoinnin olleen suhteellisen onnistunutta ja kaikkiaan monipuolisen kriittistä. Julkaistujen sotauutisten analyysi tukee tätä väittämää. Työn johtopäätösten perusteella vaikuttaa siltä, että Yhdysvaltain armeijan informaatio-ohjailua suuremmaksi ongelmaksi Irakin ja Persianlahden sotauutisoinnissa osoittautui viestinten keskinäinen kilpailuasetelma ja taloudelliset sidonnaisuudet. Omaksi ongelmakseen kasvoi myös teknologinen kehitys, joka aiheutti viestimille jatkuvan tarpeen reaaliaikaiseen, joskin tarkistamattomaan ja taustoittamattomaan uutisointiin

Negative tunneling magnetoresistance by canted magnetization in MgO/NiO tunnel barriers

The influence of insertion of an ultra-thin NiO layer between the MgO barrier and ferromagnetic electrode in magnetic tunnel junctions has been investigated by measuring the tunneling magnetoresistance and the X-ray magnetic circular dichroism (XMCD). The magnetoresistance shows a high asymmetry with respect to bias voltage, giving rise to a negative value of -16% at 2.8 K. We attribute this to the formation of non-collinear spin structures in the NiO layer as observed by XMCD. The magnetic moments of the interface Ni atoms tilt from the easy axis due to exchange interaction and the tilting angle decreases with increasing the NiO thickness. The experimental observations are further support by non-collinear spin density functional theory

Understanding Symmetry Breaking in Twisted Bilayer Graphene from Cluster Constraints

Twisted bilayer graphene is an exciting platform for exploring correlated quantum phases, extremely tunable with respect to both the single-particle bands and the interaction profile of electrons. Here, we investigate the phase diagram of twisted bilayer graphene as described by an extended Hubbard model on the honeycomb lattice with two fermionic orbitals (valleys) per site. Besides the special extended {\it cluster interaction} $Q$, we incorporate the effect of gating through an onsite Hubbard-interaction $U$. Within Quantum Monte Carlo (QMC), we find valence-bond-solid, N\'eel-valley antiferromagnetic or charge-density wave phases. Further, we elucidate the competition of these phases by noticing that the cluster interaction induces an exotic constraint on the Hilbert space, which we dub {\it the cluster rule}, in analogy to the famous pyrochlore spin-ice rule. Formulating the perturbative Hamiltonian by projecting into the cluster-rule manifold, we perform exact diagonalization and construct the fixed-point states of the observed phases. Finally, we compute the local electron density patterns as signatures distinguishing these phases, which could be observed with scanning tunneling microscopy. Our work capitalizes on the notion of cluster constraints in the extended Hubbard model of twisted bilayer graphene, and suggests a scheme towards realization of several symmetry-breaking insulating phases in a twisted-bilayer graphene sheet.Comment: 10 pages, 6 figure

Evaluating Fire Temperatures During a Prescribed Burn of a Restored Tallgrass Prairie

Wildfire is recognized to have shaped the great prairies of the central US. While the vast majority of these grasslands have been lost there remain significant remnants as well as sites under active restoration. Prescribed fire is often used in these systems in order to maximize the success of the native grasses. Beginning in 1999 Cedarville University established a prairie restoration site and have used disturbances, such as fire, to maintain the system. Without this regular burn, the prairie would likely show decreased grass growth and increased growth of forb species. The Cedarville Prairie Restoration site has a variable topography, with several small hills and valleys. Such variations can affect the way that fire travels and burns. Therefore, our objective is to evaluate the relationships between prairie topography and fire temperature. We will use a 25 x 25 meter grid within the prairie, placing stakes attached to tags painted with thermo-sensitive paint at regular intervals along the grid. Following the prescribed fire in early April we will we analyze the tags to determine the temperature of the fire at each location on the grid. From this we will generate a heat intensity map in order to investigate patterns. In particular, we anticipate that the fire will burn at higher temperatures on slopes upward from its point of origin. We also anticipate that the fire will burn at lower temperatures in valley areas, due to moisture accumulation

Algorithmic Error Mitigation Scheme for Current Quantum Processors

We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos method. This technique can reduce the impact of different sources of noise at the sole cost of an increase in the number of measurements to be performed on the target quantum circuit, without additional experimental overhead. We demonstrate through numerical simulations and experiments on IBM Quantum hardware that the proposed scheme significantly increases the accuracy of cost functions evaluations within the framework of variational quantum algorithms, thus leading to improved ground-state calculations for quantum chemistry and physics problems beyond state-of-the-art results