Carmelo J M P, Sacramento P D, Machado J D P, Campbell D K
J Phys Condens Matter. 2015 Oct 14;27(40):406001. doi: 10.1088/0953-8984/27/40/406001.
We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the 'pseudofermion dynamical theory' (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζ(τ)(k) controlling the singularities for both the longitudinal (τ = l) and transverse (τ = t) dynamical structure factors for the whole momentum range k ∈ ]0,π[, in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.
我们研究了有限磁场h下自旋为1/2的XXX链的纵向和横向自旋动力学结构因子，特别关注较低阈值附近激发能量处的奇点。虽然该模型的静态性质可以在费米液体类描述中，用赝粒子来研究，但我们对动力学性质的推导依赖于引入一种对一维哈伯德模型的“赝费米子动力学理论”（PDT）形式，该形式针对仅含自旋的XXX链以及其他具有两个赝粒子费米点的模型进行了适当修改。具体而言，我们在热力学极限下，推导了在整个动量范围k∈]0,π[内，控制纵向（τ = l）和横向（τ = t）动力学结构因子奇点的指数ζ(τ)(k)对动量和自旋密度的精确依赖关系。这需要对定义这些指数表达式中相移的积分方程进行数值求解。我们讨论了与中子散射的关系，并建议使用精心取向的晶体对自旋链化合物进行新的实验，以检验我们的预测。
