Effect of Mitigation Measures on the Spreading of COVID-19 in Hard-Hit States

State government-mandated social distancing measures have helped to slow down the growth of the COVID-19 pandemic in the United States. Current predictive models of the development of COVID-19, especially after mitigation efforts, are largely based on extrapolating the data from other countries. Since most states enforced stay-at-home orders towards the end of March, their effect should be reflected in the death and infection counts at the end of April. Using the data available until April 25th, we investigate the change in the infection rate due to the mitigation efforts, and project death and infection counts until September, 2020, for some of the most heavily impacted states: New York, New Jersey, Michigan, Massachusetts, Illinois and Louisiana. We find that with the current mitigation efforts five of those six states reduce their reproduction number to a value less than one, stopping the exponential growth of the pandemic. We also projected different scenarios after the mitigation is relaxed. Analysis for other states can be found at https://covid19projection.org/.Comment: 8 pages, 6 figures, 2 table

Identifying structural changes with unsupervised machine learning methods

Unsupervised machine learning methods are used to identify structural changes using the melting point transition in classical molecular dynamics simulations as an example application of the approach. Dimensionality reduction and clustering methods are applied to instantaneous radial distributions of atomic configurations from classical molecular dynamics simulations of metallic systems over a large temperature range. Principal component analysis is used to dramatically reduce the dimensionality of the feature space across the samples using an orthogonal linear transformation that preserves the statistical variance of the data under the condition that the new feature space is linearly independent. From there, k-means clustering is used to partition the samples into solid and liquid phases through a criterion motivated by the geometry of the reduced feature space of the samples, allowing for an estimation of the melting point transition. This pattern criterion is conceptually similar to how humans interpret the data but with far greater throughput, as the shapes of the radial distributions are different for each phase and easily distinguishable by humans. The transition temperature estimates derived from this machine learning approach produce comparable results to other methods on similarly small system sizes. These results show that machine learning approaches can be applied to structural changes in physical systems

Dominant Superconducting Fluctuations in the One-Dimensional Extended Holstein-Extended Hubbard model

The search for realistic one-dimensional (1D) models that exhibit dominant superconducting (SC) fluctuations effects has a long history. In these 1D systems, the effects of commensurate band fillings--strongest at half-filling--and electronic repulsions typically lead to a finite charge gap and the favoring of insulating density wave ordering over superconductivity. Accordingly, recent proposals suggesting a gapless metallic state in the Holstein-Hubbard (HH) model, possibly superconducting, have generated considerable interest and controversy, with the most recent work demonstrating that the putative dominant superconducting state likely does not exist. In this paper we study a model with non-local electron-phonon interactions, in addition to electron-electron interactions, this model unambiguously possesses dominant superconducting fluctuations at half filling in a large region of parameter space. Using both the numerical multi-scale functional renormalization group for the full model and an analytic conventional renormalization group for a bosonized version of the model, we demonstrate the existence of dominant superconducting (SC) fluctuations. These dominant SC fluctuations arise because the spin-charge coupling at high energy is weakened by the non-local electron-phonon interaction and the charge gap is destroyed by the resultant suppression of the Umklapp process. The existence of the dominant SC pairing instability in this half-filled 1D system suggests that non-local boson-mediated interactions may be important in the superconductivity observed in the organic superconductors.Comment: 8 pages, 4 figure

The Boson-Hubbard Model on a Kagome Lattice with Sextic Ring-Exchange Terms

High order ring-exchange interactions are crucial for the study of quantum fluctuations on highly frustrated systems. We present the first exact quantum Monte Carlo study of a model of hard-core bosons with sixth order ring-exchange interactions on a two-dimensional kagome lattice. By using the Stochastic Green Function algorithm, we show that the system becomes unstable in the limit of large ring-exchange interactions. It undergoes a phase separation at all fillings, except at 1/3 and 2/3 fillings for which the superfluid density vanishes and an unusual mixed valence bond and charge density ordered solid is formed.Comment: 4 pages, 7 figure

Functional renormalization group analysis of the half-filled one-dimensional extended Hubbard model

We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.First author draf