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Abstract We investigate the boundary phenomena that arise in a finite-sizeXXspin chain interacting through anXXinteraction with a spin $-\frac{1}{2}$impurity located at its edge. Upon Jordan–Wigner transformation, the model is described by a quadratic Fermionic Hamiltonian. Our work displays, within this ostensibly simple model, the emergence of the Kondo effect, a quintessential hallmark of strongly correlated physics. We also show how the Kondo cloud shrinks and turns into a single particle bound state as the impurity coupling increases beyond a critical value. In more detail, using bothBethe Ansatzandexact diagonalizationtechniques, we show that the local moment of the impurity is screened by different mechanisms depending on the ratio of the boundary and bulk coupling $\frac{J_{\mathrm{imp}}}{J}$. When the ratio falls below the critical value $\sqrt{2}$, the impurity is screened via the Kondo effect. However, when the ratio between the coupling exceeds the critical value $\sqrt{2}$an exponentially localized bound mode is formed at the impurity site which screens the spin of the impurity in the ground state. We show that the boundary phase transition is reflected in local ground state properties by calculating the spinon density of states, the magnetization at the impurity site in the presence of a global magnetic field, and the finite temperature susceptibility of the impurity. We find that the spinon density of states in the Kondo phase has the characteristic Lorentzian peak that moves from the Fermi level to the maximum energy of the spinon as the impurity coupling is increased and becomes a localized bound mode in the bound mode phase. Moreover, the impurity magnetization and the finite temperature impurity susceptibility behave differently in the two phases. When the boundary coupling $J_{\mathrm{imp}}$exceeds the critical value $\sqrt{2}J$, the model is no longer boundary conformal invariant as a massive bound mode appears at the impurity site. 

Abstract The COVID-19 outbreak is a global pandemic declared by the World Health Organization, with rapidly increasing cases in most countries. A wide range of research is urgently needed for understanding the COVID-19 pandemic, such as transmissibility, geographic spreading, risk factors for infections, and economic impacts. Reliable data archive and sharing are essential to jump-start innovative research to combat COVID-19. This research is a collaborative and innovative effort in building such an archive, including the collection of various data resources relevant to COVID-19 research, such as daily cases, social media, population mobility, health facilities, climate, socioeconomic data, research articles, policy and regulation, and global news. Due to the heterogeneity between data sources, our effort also includes processing and integrating different datasets based on GIS (Geographic Information System) base maps to make them relatable and comparable. To keep the data files permanent, we published all open data to the Harvard Dataverse ( https://dataverse.harvard.edu/dataverse/2019ncov ), an online data management and sharing platform with a permanent Digital Object Identifier number for each dataset. Finally, preliminary studies are conducted based on the shared COVID-19 datasets and revealed different spatial transmission patterns among mainland China, Italy, and the United States.