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Probing the antiferromagnetic long-range order with Glauber spin states

G. G. Cabrera

Published May 1, 1994• 0 citations
OpenAlex

Abstract

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.

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•Jan 1, 1991•0 citations
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.
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.
When quantum effects are small, Heisenberg antiferromagnets have a Néel ordered ground state, but strong zero-point fluctuations can lead to new ‘‘exotic’’ spin-liquid ground states without long-range Néel order. These effects are strongest in low dimensions and frustrated systems, and always occur in one dimension. The nature of the new ground state can depend on whether the microscopic spins have integer or half-integer S. As an example of such systems the rich phase diagram of the one-dimensional S=1 Heisenberg antiferromagnet with additional biquadratic exchange and uniaxial on-site anisotropy will be discussed in detail.
Antiferromagnetic Heisenberg integer-spin chains are characterized by a spin-liquid ground state with no long-range order, due to the relevance of quantum fluctuations. Spin anisotropy, however, freezes quantum fluctuations, and the system is magnetized in the presence of a sufficiently large easy-axis anisotropy. We numerically investigate the case S=1, by means of the density-matrix renormalization group, and find that the freezing of the spin liquid into a Néel spin solid, with increasing easy-axis anisotropy, is a continuous quantum phase transition. Numerical evidence indicates that the transition is not in the two-dimensional Ising universality class.
We have studied via a Green-function Monte Carlo (GFMC) method the S=(1/2 Heisenberg quantum antiferromagnet in two dimensions. We use a well-known transformation to map the spin problem onto a system of hard-core bosons that allows us to exploit interesting analogies between magnetism and superfluidity. The GFMC method is a zero-temperature stochastic method that projects out the component of the true ground state in a given variational wave function. This method is complementary to previously used finite-temperature Monte Carlo methods and is well suited to studying the ground state and low-lying excited states. Starting with even a simple wave function, e.g., the classical N\'eel state, the GFMC method can obtain the short-range correlations very accurately, and we find the ground-state energy per site E0{\mathit{E}}_{0}E0​/J=-0.6692(2). We show that it is important to include the zero-point motion of the elementary excitations in the ground state and by a spin-wave analysis find that it produces long-range correlations in the wave function. Upon inclusion of such long-range correlations, we obtain a staggered magnetization ${\mathit{m}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$=0.31(2) and the structure factor scrS(q)\ensuremath{\sim}q at long wavelengths. Using the Feynman-Bijl relation, from the slope we deduce the renormalization of the spin-wave velocity by quantum fluctuations to be Zc{\mathit{Z}}_{\mathit{c}}Zc​==c/cs{\mathit{c}}_{\mathit{s}}cs​=1.14(5).
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.