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

Significance Theoretical efforts to understand the superconducting cuprates have focused on a few simplified but challenging models: notably the Hubbard and the t-t′-J models. Using density matrix renormalization group (DMRG) simulations on width-8 cylinders, we study the ground-state phase diagram of the t-t′-J model. The next nearest-neighbor hopping t′ allows one to distinguish between hole (t′<0) and electron doping (t′>0). We find for the magnetic, charge, and single-particle properties that this model roughly captures the differences between the electron- and hole-doped cuprates. However, the superconducting properties differ. For hole doping (t′<0), there is an absence of superconductivity, while for electron doping (t′> 0), we find d-wave superconductivity coexisting with antiferromagnetism and a secondary triplet p-wave pairing component. 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.