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arXiv:cond-mat/9410105 · Journal of Physics Condensed Matter

Static structure factors of the XXZ-model in the presence of a uniform field

Michael Karbach, K -H Mutter, M Schmidt

Published Apr 3, 1995• 6 citations
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Abstract

The static structure factors of the XXZ-model in the presence of a uniform field are determined from an exact computation of the ground states at given total spin on rings with N=4,6,...,28 sites. Against the naive expectation, a weak uniform field strengthens the antiferromagnetic order in the transverse structure factor for the isotropic case.

DOI
10.1088/0953-8984/7/14/020

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The static structure factors of the XXZ-model in the presence of a uniform field are determined from an exact computation of the ground states at given total spin on rings with N=4,6,...,28 sites. Against the naive expectation, a weak uniform field strengthens the antiferromagnetic order in the transverse structure factor for the isotropic case.
The transverse and longitudinal structure factors of the spin-1/2 XXZ model are determined from a complete diagonalization of the Hamiltonian on rings with N=4,...,16 sites. At fixed critical momentum p=\ensuremath{\pi}, we observe the critical low-temperature behavior as it is predicted by scaling arguments. Finite-size scaling works well for the transverse structure factors. However, it breaks down for the longitudinal structure factors if the anisotropy is too large (\ensuremath{\gamma}>0.3\ensuremath{\pi}). We also investigate the low-temperature behavior of the uniform susceptibility.
In the presence of a uniform field the one-dimensional spin-1/2 antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent ``soft-mode'' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory. \textcopyright{} 1996 The American Physical Society.
On the basis of a numerical computation of the ground states in the sectors with a given total spin S we study the magnetic properties of the one-dimensional frustrated antiferromagnetic Heisenberg model at zero temperature and at the spin-fluid - dimer phase transition. We find that the magnetization curve M(B) has a quartic-root singularity near saturation, . The longitudinal spin - spin, the dimer - dimer and the transverse spin - spin structure factors develop singularities at the field-dependent momenta and , respectively. The type of each of these singularities depends on the frustration parameter and the magnetization M.
The exact factorized ground state of a heterogeneous (ferrimagnetic) spin model which is composed of two spins (ρ, σ) has been presented in detail. The Hamiltonian is not necessarily translational invariant and the exchange couplings can be competing antiferromagnetic and ferromagnetic arbitrarily between different sublattices to build many practical models such as dimerized and tetramerized materials and ladder compounds. The condition to get a factorized ground state is investigated for non-frustrated spin models in the presence of a uniform and a staggered magnetic field. According to the lattice model structure we have categorized the spin models in two different classes and obtained their factorization conditions. The first class contains models in which their lattice structures do not provide a single uniform magnetic field to suppress the quantum correlations. Some of these models may have a factorized ground state in the presence of a uniform and a staggered magnetic field. However, in the second class there are several spin models in which their ground state could be factorized whether a staggered field is applied to the system or not. For the latter case, in the absence of a staggered field the factorizing uniform field is unique. However, the degrees of freedom for obtaining the factorization conditions are increased by adding a staggered magnetic field.