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International Journal of Modern Physics B

On the Projected Fermion Description of Anisotropic S=1/2 Antiferromagnets

Theodore C. Hsu

Published Dec 1, 1989• 0 citations
Publisher

Abstract

In this paper we consider anisotropic S=1/2 antiferromagnets through a projected fermion description. The success of projected fermion methods for the isotropic system is reviewed. We present an analytical approximation to Gutzwiller approximation and illustrate it’s use by showing that it is consistent with the SU(2) symmetry of projected fermions. The anisotropic antiferromagnet is written in terms of a fermion mean field. We consider the case of Ising anisotropy and show that in the Ising limit a procedure of minimizing the post-projection energy of a fermion mean field state gives the correct Ising ground state.

DOI
10.1142/s0217979289001287

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In this paper we consider anisotropic S=1/2 antiferromagnets through a projected fermion description. The success of projected fermion methods for the isotropic system is reviewed. We present an analytical approximation to Gutzwiller approximation and illustrate it’s use by showing that it is consistent with the SU(2) symmetry of projected fermions. The anisotropic antiferromagnet is written in terms of a fermion mean field. We consider the case of Ising anisotropy and show that in the Ising limit a procedure of minimizing the post-projection energy of a fermion mean field state gives the correct Ising ground state.
The anisotropic Heisenberg model has been investigated by interpolating anisotropy between the Ising and isotropic Heisenberg limits via general spin high temperature series (HTS) for the zero-field susceptibility of the ferromagnets for the square lattice. This is done by locating the critical temperature ( T c (2) ) and the susceptibility exponent (γ) from the analysis of the series by Pade approximant and ratio methods. The critical temperature is found to be spin dependent. It decreases as anisotropy changes from the Ising limit towards the isotropic limit and remains finite (lower than that of Stanley and Kaplan) for all the spins except for S =1/2 at the isotropic limit. Exponent γ is almost Ising like for the anisotropic system and anomalous jump in it occurs for the isotropic case. In addition, expressions for the magnetization are derived by using spin-wave theory. The limit of complete isotropy has been found not to be a special case for the susceptibility, in contrast to magnetization.
We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.
We develop a large-N expansion for Gutzwiller projected spin states. We consider valence-bond singlets, constructed by Schwinger bosons or fermions, which are variational ground states for quantum antiferromagnets. This expansion is simpler than the familiar expansions of the quantum Heisenberg model, and thus more instructive. The diagrammatic rules of this expansion allow us to prove certain identities to all orders in 1/N. We derive the on-site spin-fluctuations sum rule for arbitrary N. We calculate the correlations of the one-dimensional valence-bond solid states and the Gutzwiller projected Fermi gas up to order 1/N. For the boson case, we are surprised to find that the mean-field, the order-1/N, and the exact correlations are simply proportional. For the fermion case, the 1/N correction enhances the zone-edge singularity. The comparison of our leading-order terms to known results for N=2 enhances our understanding of large-N approximations in general.
We propose a coherent-state solution for the one-dimensional antiferromagnetic Heisenberg Hamiltonian in the quasi-Ising asymptotic regime. We discuss the nature of the spectrum and the eigenvectors as a function of the anisotropy parameter. Results for the energy of the ground state and the short-range-order correlation agree with exact numerical calculations in a wide range of variation of anisotropy. We also present a canonical formulation of the theory which interpolates continuously from the Ising limit to cases of lower anisotropies, thus yielding a novel view of antiferromagnetism. Finally we discuss possible connections with the theory of superconductivity of high-Tc{T}_{c}Tc​ ceramics.