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1. Global phase diagram of D-wave superconductivity in the square-lattice t-J model.

   https://doi.org/10.1073/pnas.2420963122  

   Chen, Feng; Haldane, F_D M; Sheng, D N (March 2025, Proceedings of the National Academy of Sciences)

   The Hubbard and closely relatedt-Jmodels are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extendedt-Jmodel on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the puret-Jmodel with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( $\delta =0.1\mathrm{to}0.2$), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping $t_2$suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates thet-Jmodel as a proper minimum model for the emergence of superconductivity in cuprate superconductors. 

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2. Ground-state phase diagram of the t-t ′ -J model

   https://doi.org/10.1073/pnas.2109978118  

   Jiang, Shengtao; Scalapino, Douglas J.; White, Steven R. (November 2021, Proceedings of the National Academy of Sciences)

   We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t - t ′ - J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative t ′ values ( t ′ / t = ± 0.2 ) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The t ′ < 0 (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find t ′ < 0 strongly suppresses superconductivity. The t ′ > 0 (electron-doped) region shows the expected circular Fermi pocket of holes around the ( π , π ) point and a broad low-doped region of coexisting antiferromagnetism and d -wave pairing with a triplet p component at wavevector ( π , π ) induced by the antiferromagnetism and d -wave pairing. The pairing for the electron low-doped system with t ′ > 0 is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d -wave pairing and striped p -wave pairing appears. In a small doping region near x = 0.08 for t ′ ∼ − 0.2 , we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders. 

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3. Tuning from failed superconductor to failed insulator with magnetic field

   https://doi.org/10.1126/sciadv.aav7686  

   Li, Yangmu; Terzic, J.; Baity, P. G.; Popović, Dragana; Gu, G. D.; Li, Qiang; Tsvelik, A. M.; Tranquada, J. M. (June 2019, Science Advances)

   Do charge modulations compete with electron pairing in high-temperature copper oxide superconductors? We investigated this question by suppressing superconductivity in a stripe-ordered cuprate compound at low temperature with high magnetic fields. With increasing field, loss of three-dimensional superconducting order is followed by reentrant two-dimensional superconductivity and then an ultraquantum metal phase. Circumstantial evidence suggests that the latter state is bosonic and associated with the charge stripes. These results provide experimental support to the theoretical perspective that local segregation of doped holes and antiferromagnetic spin correlations underlies the electron-pairing mechanism in cuprates. 

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4. Doping asymmetry in the three-band Hamiltonian for cuprate ladders: Failure of the standard model of superconductivity in cuprates

   https://doi.org/10.1103/PhysRevB.107.L241108  

   Song, Jeong-Pil; Mazumdar, Sumit; Clay, R. Torsten (June 2023, Physical Review B)

   Stephen E. Nagler (Ed.)

   The relevance of the single-band two-dimensional Hubbard model to superconductivity in the doped cuprates has recently been questioned, based on density matrix renormalization group (DMRG) computations that found superconductivity over an unrealistically broad doping region upon electron-doping, yet a complete absence of superconductivity for hole-doping. We report very similar results from DMRG calculations on a Cu2O3 twoleg ladder within the parent three-band correlated-electron Hamiltonian. The strong asymmetry found in our calculations are in contradiction to the deep and profound symmetry in the experimental phase diagrams of electron- and hole-doped cuprate superconductors, as seen from the occurrence of quantum critical points within the superconducting domes in both cases that are characterized by Fermi surface reconstruction, large jumps in carrier density, and strange metal behavior. 

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5. Emergence of quasiparticles in a doped Mott insulator

   https://doi.org/10.1038/s42005-020-00480-5  

   Wang, Yao; He, Yu; Wohlfeld, Krzysztof; Hashimoto, Makoto; Huang, Edwin W; Lu, Donghui; Mo, Sung-Kwan; Komiya, Seiki; Jia, Chunjing; Moritz, Brian; et al (December 2020, Communications Physics)

   Abstract How a Mott insulator develops into a weakly coupled metal upon doping is a central question to understanding various emergent correlated phenomena. To analyze this evolution and its connection to the high-T_ccuprates, we study the single-particle spectrum for the doped Hubbard model using cluster perturbation theory on superclusters. Starting from extremely low doping, we identify a heavily renormalized quasiparticle dispersion that immediately develops across the Fermi level, and a weakening polaronic side band at higher binding energy. The quasiparticle spectral weight roughly grows at twice the rate of doping in the low doping regime, but this rate is halved at optimal doping. In the heavily doped regime, we find both strong electron-hole asymmetry and a persistent presence of Mott spectral features. Finally, we discuss the applicability of the single-band Hubbard model to describe the evolution of nodal spectra measured by angle-resolved photoemission spectroscopy (ARPES) on the single-layer cuprate La_2−xSr_xCuO₄(0 ≤x≤ 0.15). This work benchmarks the predictive power of the Hubbard model for electronic properties of high-T_ccuprates. 

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