用几乎守恒量表示的Drude权的热力学界
Thermodyamic bounds on Drude weights in terms of almost-conserved quantities
摘要：
我们考虑一维量子自旋（或费米子）晶格和证明Mazur型不等式约束的时间平均的热力学极限的有限温度期望的时空自相关函数的局部观察准局部守恒律与开放边界条件。也就是说，哈密顿量和有限链的守恒定律之间的交换子可能只产生边界项。本书没有提到铃木证明马祖尔界时所使用的技巧（它严格地只适用于具有精确守恒律的有限尺寸系统），而是引用了准定域C^* 量子自旋代数的李伯-罗宾逊界和指数聚类定理。我们的结果在量子自旋链的输运理论中有重要的应用，特别是它提供了各向异性Heisenberg XXZ自旋1/2链中正的有限温度自旋Drude重量的严格非平凡例子[Phys. Rev. Lett. 106，217206（2011）]。
英文摘要：
We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki's proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C^* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain [Phys. Rev. Lett. 106, 217206 (2011)].
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