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Physical review. B, Condensed matter

Self-consistent study of quantum spin fluctuations in the Mott-Hubbard antiferromagnet

Avinash Singh

Published Sep 1, 1993• 0 citations
Publisher

Abstract

A self-consistent method for studying quantum spin fluctuations in the Mott-Hubbard antiferromagnet is presented within a diagrammatic scheme. The treatment involves the self-consistently renormalized one-particle Green's function (including its incoherent spectral part), and the renormalized spin-wave propagator, the exact long-wavelength form of which follows from an identity related to the commutation properties of spin-angular-momentum operators. In two dimensions, for the square-lattice case, we obtain M(0)=0.62 for the zero-temperature sublattice magnetization.

DOI
10.1103/physrevb.48.7700

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A self-consistent method for studying quantum spin fluctuations in the Mott-Hubbard antiferromagnet is presented within a diagrammatic scheme. The treatment involves the self-consistently renormalized one-particle Green's function (including its incoherent spectral part), and the renormalized spin-wave propagator, the exact long-wavelength form of which follows from an identity related to the commutation properties of spin-angular-momentum operators. In two dimensions, for the square-lattice case, we obtain M(0)=0.62 for the zero-temperature sublattice magnetization.
We introduce a slave-fermion formulation in which to study the charge dynamics of the half-filled Hubbard model on the square lattice. In this description, the charge degrees of freedom are represented by fermionic holons and doublons and the Mott-insulating characteristics of the ground state are the consequence of holon–doublon bound-state formation. The bosonic spin degrees of freedom are described by the antiferromagnetic Heisenberg model, yielding long-ranged (Néel) magnetic order at zero temperature. Within this framework and in the self-consistent Born approximation, we perform systematic calculations of the average double occupancy, the electronic density of states, the spectral function and the optical conductivity. Qualitatively, our method reproduces the lower and upper Hubbard bands, the spectral-weight transfer into a coherent quasiparticle band at their lower edges and the renormalisation of the Mott gap, which is associated with holon–doublon binding, due to the interactions of both quasiparticle species with the magnons. The zeros of the Green function at the chemical potential give the Luttinger volume, the poles of the self-energy reflect the underlying quasiparticle dispersion with a spin-renormalised hopping parameter and the optical gap is directly related to the Mott gap. Quantitatively, the square-lattice Hubbard model is one of the best-characterised problems in correlated condensed matter and many numerical calculations, all with different strengths and weaknesses, exist with which to benchmark our approach. From the semi-quantitative accuracy of our results for all but the weakest interaction strengths, we conclude that a self-consistent treatment of the spin-fluctuation effects on the charge degrees of freedom captures all the essential physics of the antiferromagnetic Mott–Hubbard insulator. We remark in addition that an analytical approximation with these properties serves a vital function in developing a full understanding of the fundamental physics of the Mott state, both in the antiferromagnetic insulator and at finite temperatures and dopings.
We present an approach to the magnetic properties of the half-filled Hubbard model, based on an approximate mapping of its low-energy transverse spin excitations on to those of an effective underlying Heisenberg model, but with effective spin interactions which are self-consistently determined and not confined solely to nearest-neighbor couplings. The mapping is exact in strong-coupling and is found to be accurate over a very wide range of interaction strengths, down to weak coupling. At zero temperature, it permits ready evaluation at finite U of the one-loop effects of zero-point spin fluctuations on, e.g., the sublattice magnetization. At finite temperatures, thermodynamic properties of the system in the thermal paramagnet are studied via a physically transparent Onsager reaction field approach, which amounts to a self-consistent treatment of paramagnetic spin correlations. This is central not only in recovering the correct dimensionality dependence of antiferromagnetic long-ranged order, but also for the d=3 case of primary interest here yields a N\'eel temperature in close agreement with known strong- and weak-coupling limits. Spin correlation functions and magnetic susceptibilities also show very good agreement with quantum Monte Carlo calculations over an appreciable temperature range in which the low-lying transverse spin excitations are thermally dominant. \textcopyright{} 1996 The American Physical Society.
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A self-consistent theory of both spin and charge fluctuations in the Hubbard model is presented. It is in quantitative agreement with Monte Carlo data at least up to intermediate coupling (U\ensuremath{\sim}8t). It includes both short-wavelength quantum renormalization effects, and long-wavelength thermal fluctuations, which can destroy long-range order in two dimensions. The last effect leads to a small energy scale, as often observed in high-temperature superconductors. The theory is conserving, satisfies the Pauli principle, and includes three-particle correlations necessary to account for the incipient Mott transition.
We analyze the role of spatial electronic correlations and, in particular, of the magnetic fluctuations in Mott insulators. A half-filled Hubbard model is solved at large strength of the repulsion UUU on a two-dimensional square lattice using an advanced diagrammatic approach capable of going beyond Hartree-Fock and single-site dynamical mean-field theories. We show that at high temperatures, when the magnetic fluctuations are weak, the electronic self-energy of the system is mainly local and is well reproduced by the atomic (Hubbard-I) approximation. Upon lowering the temperature toward the magnetically ordered phase, the nonlocality of the self-energy becomes crucial in determining the momentum dispersion of the Hubbard bands and the Green's function zeros. We therefore establish a precise link between Luttinger surface, nonlocal correlations and spectral properties of the Hubbard bands.