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The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature (Tc) superconductivity.more » « less
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Qin, Mingpu; Schäfer, Thomas; Andergassen, Sabine; Corboz, Philippe; Gull, Emanuel (, Annual Review of Condensed Matter Physics)The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics or the fruit fly to biomedical science. Despite its simplicity, the model exhibits an incredible wealth of phases, phase transitions, and exotic correlation phenomena. Although analytical methods have provided a qualitative description of the model in certain limits, numerical tools have shown impressive progress in achieving quantitative accurate results over the past several years. This article gives an introduction to the model, motivates common questions, and illustrates the progress that has been achieved over recent years in revealing various aspects of the correlation physics of the model.more » « less
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Chung, Chia-Min; Qin, Mingpu; Zhang, Shiwei; Schollwöck, Ulrich; White, Steven R. (, Physical Review B)