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Physical review. B, Condensed matter

Phase separation in the large-Nlimit of thet-Jmodel

M. Grilli, Claudio Castellani, Gabriel Kotliar

Published May 1, 1992• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.45.10805

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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.
The phase diagram of the 2D t-J model is investigated using high-temperature expansions. Series for the Helmholtz free energy, the inverse compressibility, the chemical potential, and the uniform spin susceptibility through tenth order are calculated and analyzed. A region of phase separation is found at T=0 for J/t lying above a line extending from J/t=3.8 at zero filling to J/t=1.2 at half filling. For very small J/t near half filling where the Nagaoka effect is possible, we find a region of divergent uniform magnetic susceptibility at T=0.
It is shown that, for the t-J model, dilute holes in an antiferromagnet are unstable against phase separation into a hole-rich and a no-hole phase. When the spin-exchange interaction J exceeds a critical value Jc{J}_{c}Jc​, the hole-rich phase has no electrons. It is proposed that for J slightly less than Jc{J}_{c}Jc​ the hole-rich phase is a low-density superfluid of electron pairs. A brief discussion of phase separation in other related models is given.
To gain insight into the behavior of the Hubbard model, we define a SU(n)\mathrm{SU}(n)SU(n) invariant generalization of the Hubbard-Heisenberg model and, in the large-nnn limit, solve it in one dimension and in two dimensions on a square lattice. In one dimension the ground state is completely dimerized near half filling. We show that this behavior agrees with a renormalization-group solution of the one-dimensional SU(n)\mathrm{SU}(n)SU(n) Hubbard model. In two spatial dimensions we find several different ground states depending on the size of the hopping term ttt, the doping $\ensuremath{\delta}$, and the biquadratic spin interaction $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$. In particular, the undimerized "flux" or "s+ids+ids+id" phase is the ground state at half filling for sufficiently large ttt or $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$. We study the electronic and spin excitations of the various phases and comment on the relevance of the large-nnn problem to the high-Tc{T}_{c}Tc​ superconductors.
We investigate the phase diagram of the two-dimensional t-J model using a recently developed Green's function Monte Carlo method for lattice fermions. We use the technique to calculate exact ground-state energies of the model on large lattices. In contrast to many previous studies, we find the model phase separates for all values of J/tJ/tJ/t. In particular, it is unstable at the hole dopings and interaction strengths at which the model was thought to describe the cuprate superconductors.