Phase Separation in a t - J Model

Alexander A. Gorbatsevich, S.V. Zaykov

Steven R. White, Douglas J. Scalapino

We make a critical analysis of numerical results for and against phase separation and stripe formation in the $t\ensuremath{-}J$ model. We argue that the frustrated phase separation mechanism for stripe formation requires phase separation at too high a doping for it to be consistent with existing numerical studies of the $t\ensuremath{-}J$ model. We compare variational energies for various methods, and conclude that the most accurate calculations for large systems appear to be from the density-matrix renormalization group. These calculations imply that the ground state of the doped $t\ensuremath{-}J$ model is striped, not phase separated.

C. T. Shih, Y. C. Chen, T. K. Lee

M. Grilli, Claudio Castellani, Gabriel Kotliar

We study the phase diagram of the SU(N) t-J model. The model has been investigated in the N=\ensuremath{\infty} limit, analyzing various magnetic phases with cell doubling (dimer, flux, and uniform). We find a phase separation between a fully dimerized phase at half-filling and a hole-rich uniform phase supporting the occurrence of phase separation in the t-J model between a Fermi-liquid phase and an insulating magnetic phase.

C. Stephen Hellberg, Efstratios Manousakis

Elbio R. Dagotto, José A. Riera, Y.-C. Chen +4 more

Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques, we have found indications that the two-dimensional t-J model superconducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera [Phys. Rev. Lett. 70, 682 (1993)]. At this density the dominant channel is ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-${\mathit{T}}_{\mathit{c}}$ cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.