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Physical review. B, Condensed matter

Mean-field theory for thet-Jmodel

Ciriyam Jayaprakash, H. R. Krishnamurthy, Sanjoy Kumar Sarker

Published Aug 1, 1989• 186 citations
Publisher

Abstract

We present a new mean-field theory for the t-J model using a representation in which singly occupied sites or spins are represented by bosons and empty sites or holes by fermions. We obtain a phase diagram which includes ferromagnetic, antiferromagnetic, spiral (with the pitch inversely proportional to the density of holes), and disordered spin-liquid phases, with a clear separation of charge and spin excitations. We comment on the conditions for obtaining superconductivity in the model.

DOI
10.1103/physrevb.40.2610

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Doped carrier formulation and mean-field theory of the tt′t″J model

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We show that the phase diagram and the odd p-wave quasiparticle gap for spinless fermions obtained in the paper by Kochetov and Mierzejewski for the $t\ensuremath{-}J$ model are artifacts of the adopted spin-charge separation treated in mean field approximation, while the critical remarks concerning the theory of exchange superconducting pairing derived within the Hubbard operator approach are misleading.

Physical review. B, Condensed matter•Jul 7, 2003•0 citations
We present a new mean-field theory for the t-J model using a representation in which singly occupied sites or spins are represented by bosons and empty sites or holes by fermions. We obtain a phase diagram which includes ferromagnetic, antiferromagnetic, spiral (with the pitch inversely proportional to the density of holes), and disordered spin-liquid phases, with a clear separation of charge and spin excitations. We comment on the conditions for obtaining superconductivity in the model.
We show an exact representation of the t-J model by making use of a general Holstein-Primakoff transformation. The single occupancy constraint on the electrons is imposed strictly at every lattice site and the t-J Hamiltonian is transformed into an equivalent interacting boson and fermion system. The lowest-order approximation of a systematic perturbative expansion of the representation is shown to correspond to the mean-field theory of the Schwinger-boson approach. The second-order approximation gives the magnon-magnon, magnon-hole, and hole-hole interactions and the high-order antiferromagnetic spin polaron. In particular the second-order approximation takes further account of the renormalization of the magnon frequency and the antiferromagnetic spin polaron. The spectra of holes and magnons are calculated with the Green's function. The relevance of the obtained results to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors is discussed. \textcopyright{} 1996 The American Physical Society.
We investigate the single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.
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.
In the generalized-tJtJtJ model the effect of a large local Coulomb repulsion is accounted for by restricting the Hilbert space to states with at most one electron per site. In this case the electronic system can be viewed in terms of holes hopping in a lattice of correlated spins, where holes are the carriers doped into the half-filled Mott insulator. To explicitly capture the interplay between the hole dynamics and local spin correlations we derive a formulation of the generalized-tJtJtJ model where doped carrier operators are used instead of the original electron operators. This ``doped carrier'' formulation provides a starting point to address doped spin systems, and we use it to develop a fully fermionic, mean-field description of doped Mott insulators. This mean-field approach reveals a mechanism for superconductivity---namely, spinon-dopon mixing---and we apply it to the $t{t}^{\ensuremath{'}}{t}^{\ensuremath{''}}J$ model as of interest to high-temperature superconductors. In particular, we use model parameters borrowed from band calculations and from fitting angle-resolved photoemission spectroscopy data to obtain a mean-field phase diagram that reproduces semiquantitatively that of hole- and electron-doped cuprates. The mean-field approach hereby presented accounts for the local antiferromagnetic and ddd-wave superconducting correlations which, we show, provide a rational for the role of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ in strengthening superconductivity as expected by experiments and other theoretical approaches. As we discuss how ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$ affect the phase diagram, we also comment on possible scenarios to understand the differences between as-grown and oxygen-reduced electron-doped samples.