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Physical review. B, Condensed matter

Fermion mean-field solutions for the Heisenberg and thet-Jmodels

Hongguang Chi, A. D. S. Nagi

Published Jun 1, 1993• 0 citations
Publisher

Abstract

Fermion mean-field solutions for the Heisenberg and the t-J models have been obtained by considering particle-hole correlations and carrying out the mean-field-theory calculations in momentum space. At half-filling the solutions have mixed (s\ifmmode\pm\else\textpm\fi{}d)-wave-like symmetry and have a lower ground-state energy than the s (uniform phase) and the d phases. On doping, the solutions with mixed s and d symmetry still have lower ground-state energy than the uniform phase. In the presence of doping, the density of states at the Fermi level in the mixed phases is depressed from its value in the uniform phase and is in good agreement with the experimental data.

DOI
10.1103/physrevb.47.14603

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Journal of the Physical Society of Japan•Apr 15, 1994•2 citations
Fermion mean-field solutions for the Heisenberg and the t-J models have been obtained by considering particle-hole correlations and carrying out the mean-field-theory calculations in momentum space. At half-filling the solutions have mixed (s\ifmmode\pm\else\textpm\fi{}d)-wave-like symmetry and have a lower ground-state energy than the s (uniform phase) and the d phases. On doping, the solutions with mixed s and d symmetry still have lower ground-state energy than the uniform phase. In the presence of doping, the density of states at the Fermi level in the mixed phases is depressed from its value in the uniform phase and is in good agreement with the experimental data.
We study the low-energy properties of the spinful Bose-Fermi Hubbard model on a simple cubic lattice for attractive fermion-fermion and repulsive boson-boson interactions at half-filling for the fermions and unit-filling for the bosons. Recent DMFT results predict a variety of phases, including superfluids, charge density waves, mixed states and supersolids. We develop a self-consistent mean-field scheme which allows for all orders to appear and determine the ground state of the system by comparing the corresponding energies. In the double superfluid phase, we consider possibilities for exotic extended s-, p- and d-wave boson-assisted superfluidity.
We investigate the two-dimensional t-J model at a hole doping of x=18x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{8}x=81​. The low-energy states are uniform (not striped). We find numerous excited states with charge density wave structures, which may be interpreted as striped phases. Some of these are consistent with neutron scattering data on cuprates and nickelates. Without additional terms in the t-J Hamiltonian, stripes can be stabilized only as ground states through the application of artificial boundary conditions.
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.
We have applied mean-field theory to calculate the spin-density-wave (SDW) order parameter \ensuremath{\Delta}, the chemical potential \ensuremath{\mu}, and the ground-state energy at various band fillings for the Hubbard model. We have found that at zero temperature and in the large-U limit, the SDW order parameter and the ground-state energy can be written as \ensuremath{\Delta}=U(1-x)/2-O(J) and Eg{\mathit{E}}_{\mathit{g}}Eg​=-U(1-x)2{)}^{2})2/4-0(J). The chemical potential obtained here for x=0 and 1 agrees well with the result obtained by the exact-diagonalization calculation on a 4\ifmmode\times\else\texttimes\fi{}4 sites cluster by Dagotto et al. [Phys. Rev. B 45, 10 741 (1992)]. In the SDW phase, the mean-field theory gives an upward shift in the chemical potential as one dopes away from half-filling, which is in contrast with the exact-diagonalization calculations. This result indicates that the Mott-Hubbard gap is depressed much more rapidly in the mean-field theory than the exact-diagonalization calculation. The doping dependence of ground-state energy calculated here is in good agreement with the above numerical calculation for doping up to 0.5. Here, U is the intrasite Coulomb repulsion, x is doping concentration, J=4t2{\mathit{t}}^{2}t2/U is the superexchange interaction parameter, and t is the hopping integral for the nearest neighbors.
Ground states of the two-dimensional t - t '- J model with one and two holes in 4×4 sites (with periodic boundary conditions) are studied numerically. Using a Lanczos algorithm, we calculate the ground-state energy and momentum distribution, and the phase diagram in the plane of J / t and t '/ t is presented. The momentum distribution for J / t =0.25 is compared with the Fermi surface obtained in the mean-field theory. It is shown that the t '/ t dependences of the momentum distribution are consistent with the mean-field approximation, although there are quantitative differences between them.