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Modern Physics Letters B

KINETIC ENERGY AND PHASE SEPARATION IN A DOPED ANTIFERROMAGNET

Xin Xu, Yun Song, Shiping Feng

Published Oct 20, 1995• 2 citations
Publisher

Abstract

The ground-state kinetic energy of the t-J model is studied within the mean field approximation by using the fermion-spin transformation, the results show that the mean field ground-state kinetic energy is close to the numerical result at under dopings, and roughly consistent with the numerical result at optimal dopings. It is also shown that the frustration term J′ is favourable to diminish the range of the phase seperation in the t-J model.

DOI
10.1142/s0217984995001625

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The ground-state kinetic energy of the t-J model is studied within the mean field approximation by using the fermion-spin transformation, the results show that the mean field ground-state kinetic energy is close to the numerical result at under dopings, and roughly consistent with the numerical result at optimal dopings. It is also shown that the frustration term J′ is favourable to diminish the range of the phase seperation in the t-J model.
A fermion-spin transformation is used to implement the charge-spin separation, and is developed to study the low-dimensional t-J model. In this approach, the charge and spin degrees of freedom of the physical electron are separated, and the charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is representd by a hard-core boson. The on-site local constraint for single occupancy is satisfied even in the mean-field approximation and the sum rule for the physical electron is obeyed. This approach can be applied to both one and two-dimensional systems. In the one-dimensional case, the spinon as well as the physical electron behave like Luttinger liquids. We have obtained a gapless charge and spin excitation spectrum, a good ground state energy, and a reasonable electron-momentum distribution within the mean-field approximation. The correct exponents of the correlation functions and momentum distribution are also obtained if the squeezing effect and rearrangement of the spin configurations are taken into account. In the two-dimensional case, within the mean-field approximation the magnetized flux state with a gap in the spinon spectrum has the lowest energy at half filling. The antiferromagnetic long-range order is destroyed by hole doping of the order \ensuremath{\sim}10-15 % for t/J=3-5 and a disordered flux state with gapless spinon spectrum becomes stable. The calculated specific heat is roughly consistent with observed results on copper oxide superconductors. The possible phase separation is also discussed at the mean-field level.
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 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.
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Two-leg t-J ladders are investigated in the framework of a combination of the phass string formulation and bond-operator representation. We develope a mean-field theory in the strong rung interaction regime, i.e. J┴ ＞＞ J, t, which provides a unified description of the undoped insulating phase and the low doping spin gap phase. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry gap driven by the t- term. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of J/t for given doping concentration. The local structure of hole pairs as well as the spectra of various spin and charge modes are also analyzed.