Thermal Conductivity of a Heisenberg Chain
Thermal Conductivity of a Heisenberg Chain
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海森堡链的热导率
DOI：
10.1143/ptp.40.918
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发表时间：
1968
影响因子：
--
通讯作者：
D. Huber
中科院分区：
文献类型：
--
作者：
D. Huber
用热电流法计算了一维磁性晶格的导热系数。假设自旋通过最近邻的铁磁性海森堡交换相互作用耦合。电导率与六自旋关联函数成正比，该关联函数被分解为三个双自旋关联函数的乘积。在半经典近似下，假设时间呈指数衰减，对双自旋函数进行了计算。衰变速率被认为与自旋扩散常数成正比，这是从Bennett和Martin的非线性形式得到的。由此得到的电导率表达式是自旋扩散常数与经典链在整个温度范围内的比热的乘积。结合计算中的近似值讨论了这一结果的意义。还给出了一种适用于低温的替代处理方法。后一种方法导致在边界散射区内导电性随温度线性地消失。
The thermal conductivity of a one dimensional magnetic lattice is calculated in the ther mal current formalism. It is assumed that the spins are coupled by a nearest-neighbor ferromagnetic Heisenberg exchange interaction. The counductivity is shown to be propor tional to a six-spin correlation function which is factored into a product of three two-spin correlation functions. The two-spin functions are evaluated in a semi-classical approximation assuming exponential decay in time. The rate of decay is taken to be proportional to the spin diffusion constant, which is obtained from the non-linear formalism of Bennett and Martin. The resulting expression for the conductivity scales as the product of the spin diffusion con stant and the specific heat of a classical chain over the entire temperature range O<::,T«:;.oo. The significance of this result is discussed with reference to the approximations made in the calculation. An alternative treatment which is appropriate at low temperatures is also given. This latter approach leads to a conductivity which vanishes linearly with temperature in the boundary scattering region.