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Physical review. B, Condensed matter

Localized-versus-extended spin fluctuations in quantum antiferromagnets

G. G. Cabrera

Published Jun 1, 1991• 3 citations
Publisher

Abstract

A recently devised trial wave function for the Heisenberg-Ising model is tested against linear spin waves in the whole anisotropic region. The above wave function is asymptotically exact in the limit of high anisotropy, and is constructed using localized spin fluctuations over N\'eel states. The structure of this trial state is compared with the one presented by the zero-point state of the linear-spin-wave theory. Striking similarities are found between both, despite that spin waves represent fluctuations that encompass the whole system. A crossover between both approaches near the isotropic point is attributed to a delocalization of spin fluctuations. We present results for one and two dimensions, and compare with exact results or numerical simulations.

DOI
10.1103/physrevb.43.13476

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A recently devised trial wave function for the Heisenberg-Ising model is tested against linear spin waves in the whole anisotropic region. The above wave function is asymptotically exact in the limit of high anisotropy, and is constructed using localized spin fluctuations over N'eel states. The structure of this trial state is compared with the one presented by the zero-point state of the linear-spin-wave theory. Striking similarities are found between both, despite that spin waves represent fluctuations that encompass the whole system. A crossover between both approaches near the isotropic point is attributed to a delocalization of spin fluctuations. We present results for one and two dimensions, and compare with exact results or numerical simulations.
It is well known that the ground state of low-dimensional antiferromagnets deviates from Neel states due to strong quantum fluctuations. Even in the presence of long-range order, those fluctuations produce a substantial reduction of the magnetic moment from its saturation value. Numerical simulations in anisotropic antiferromagnetic chains suggest that quantum fluctuations over Neel order appear in the form of localized reversal of pairs of neighboring spins. In this paper, we propose a coherent state representation for the ground state to describe the above situation. In the one-dimensional case, our wave function corresponds to a two-mode Glauber state, when the Neel state is used as a reference, while the boson fields are associated to coherent flip of spin pairs. The coherence manifests itself through the antiferromagnetic long-range order that survives the action of quantum fluctuations. The present representation is different from the standard zero-point spin wave state, and is asymptotically exact in the limit of strong anisotropy. The fermionic version of the theory, obtained through the Jordan-Wigner transformation, is also investigated.
We present a detailed investigation of the XXZ Heisenberg model for spin-1/21/21/2 and spin-1 systems on square and honeycomb lattices. Utilizing the density-matrix renormalization group method, complemented by spiral boundary conditions (SBCs) for mapping two-dimensional (2D) clusters onto one-dimensional chains, we meticulously explore the evolution of staggered magnetization and spin gaps across a broad spectrum of easy-axis anisotropies. Our study reveals that despite the lower site coordination number of the honeycomb lattice, which intuitively suggests increased quantum fluctuations in its N\'eel phase compared to the square lattice, the staggered magnetization in the honeycomb structure exhibits only a marginal reduction. Furthermore, our analysis demonstrates that the dependence of staggered magnetization on the XXZ anisotropy $\mathrm{\ensuremath{\Delta}}$, except in close proximity to $\mathrm{\ensuremath{\Delta}}=1$, aligns with series expansion predictions up to the 12th order. Notably, for the S=1/2S=1/2S=1/2 honeycomb lattice, deviations from the 10th-order series expansion predictions near the isotropic Heisenberg limit emphasize the critical influence of quantum fluctuations on the spin excitation in its N\'eel state. Additionally, our findings are numerically consistent with the singular behavior of the spin gap near the isotropic Heisenberg limit as forecasted by spin-wave theory. The successful implementation of SBCs marks a methodological advancement, streamlining the computational complexity involved in analyzing 2D models and paving the way for more precise determinations of physical properties in complex lattice systems.
We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0)\Gamma(\mathbf q=0)Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)]\pm[\mathbf Q= (4\pi/3,0)]±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.
We develop a theory for antiferromagnetism which is asymp- totically exact in the limit of high correlation. A trial ground state wave function is obtained through a bosonization of the Heisenberg Hamiltonian in the axial-anisotropy region. This state is represented as a quantum CO- herent state displaying long-range order. Quantities of physical interest are calculated in closed analytic form and compared with exact results or numerical simulations, showing an excellent agreement in a wide range of variation of the anisotropy parameter. We discuss the limitations of our theory near the isotropic point
The isotropic Heisenberg antiferromagnet is studied using the Dyson-Maleev two-boson spin-wave model. A T=0T=0T=0 expansion in the inverse of the spin SSS is renormalized at $d=1+\ensuremath{\epsilon}$ using renormalization-group methods. The spin-wave interaction is shown to be consistently given after renormalization by the single coupling strength ${S}^{\ensuremath{-}1}$ having a fixed point of order $\ensuremath{\epsilon}$. The model is found to closely parallel the small-TTT expansion of the classical ferromagnet having fixed-length spins at $2+\ensuremath{\epsilon}$ dimensions. The implications of the result for the possibility of long-range order near d=1d=1d=1 and the structure of the spin-spin corrrelation function in this region are discussed.
The Heisenberg-Ising Hamiltonian has been exactly solved us- ing the Lanczos method, for chain of up to N = 28 spins. In the whole anisotropic region, the mass gap displays a dominant exponential behavior with size. The extrapolated ground state is doubly degenerate, and presents long-range order with dominant components of the Neel type. Quantum fluctuations become more important as long as the anisotropy is reduced, leading to a disordered singlet ground state for the infinite system at the isotropic point.