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Physical review. B, Condensed matter

Phase separation in the slave-fermion mean-field theory of thet-Jmodel

Tzanko Ivanov

Published Dec 1, 1991• 9 citations
Publisher

Abstract

The stability of the spiral phase is studied in the context of the slave-fermion mean-field theory of the t-J model. For J/t small enough the spiral phase is unstable against phase separation. For larger values of J/t there exists a critical concentration of holes below which this phase is stable, while for larger doping a phase separation occurs. The phase diagram of the t-J model is presented and discussed.

DOI
10.1103/physrevb.44.12077

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The stability of the spiral phase is studied in the context of the slave-fermion mean-field theory of the t-J model. For J/t small enough the spiral phase is unstable against phase separation. For larger values of J/t there exists a critical concentration of holes below which this phase is stable, while for larger doping a phase separation occurs. The phase diagram of the t-J model is presented and discussed.
The supersymmetric formulation of the t - J model is studied in this paper at the mean-field level where the δ- T phase diagram is determined. We found that the slave-fermion–like spiral phase is stable at low doping concentration, and the slave-boson–like d -wave fermionic spin pairing state becomes energetically favourable when δ ⩾ 0.23. An improvement in free energy using Gutzwiller's method lowers the transition doping concentration to δ ≃ 0.06. We also point out the existence of new branches of excitations in the supersymmetric theory.
We analyze a class of mean-field flux phases of the slave boson t-J model, and present a finite-temperature phase diagram. The mean-field theory arises from a decomposition of the four-fermion terms into exchange, pairing, and direct terms, using Hubbard-Stratonovich fields. We find numerically that at low doping staggered flux phases are energetically favorable over the d-wave-pairing state. Very close to half filling a \ensuremath{\pi}-flux phase becomes stable. The occurrence of flux phases suppresses the pairing gap transition temperature.
Based on the U(1) slave-boson functional integral approach to the $t\ensuremath{-}J$ model Hamiltonian, we investigate the phase diagram of phase separation for the hole-doped two-dimensional system of antiferromagnets. We discuss the phase separation (into a hole-rich and a hole-free phase) as a function of J/tJ/tJ/t where J is the Heisenberg (antiferromagnetic) coupling constant and t the hopping energy. For the physically interesting region of relatively small Heisenberg coupling, 0<J/t<0.2,0<J/t<0.2,0<J/t<0.2, we find that the phase separation occurs in a region of hole doping concentration below ${x}_{c}\ensuremath{\sim}0.1$ and that in the same region the critical hole doping concentrations remain robust with nearest-neighbor hole-hole repulsive interactions. On the other hand, in the region of larger J/tJ/tJ/t the phase separation boundary is found to be highly sensitive to the variation of the repulsive hole-hole interactions. In agreement with other studies, we find that the phase separation occurs at a critical value of ${J}_{c}\ensuremath{\approx}3.4t$ corresponding to the critical hole concentration xc=1.{x}_{c}=1.xc​=1.
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.
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.