Kobayashi Hirokazu, Watanabe Haruki
Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan.
Phys Rev Lett. 2022 Oct 21;129(17):176601. doi: 10.1103/PhysRevLett.129.176601.
For every conserved quantity written as a sum of local terms, there exists a corresponding current operator that satisfies the continuity equation. The expectation values of current operators at equilibrium define the persistent currents that characterize spontaneous flows in the system. In this Letter, we consider quantum many-body systems on a finite one-dimensional lattice and discuss the scaling of the persistent currents as a function of the system size. We show that, when the conserved quantities are given as the Noether charges associated with internal symmetries or the Hamiltonian itself, the corresponding persistent currents can be bounded by a correlation function of two operators at a distance proportional to the system size, implying that they decay at least algebraically as the system size increases. In contrast, the persistent currents of accidentally conserved quantities can be nonzero even in the thermodynamic limit and even in the presence of the time-reversal symmetry. We discuss "the current of energy current" in S=1/2 XXZ spin chain as an example and obtain an analytic expression of the persistent current.
对于每一个写成局部项之和的守恒量，都存在一个满足连续性方程的相应流算符。平衡态下流算符的期望值定义了表征系统中自发流动的持续电流。在本快报中，我们考虑有限一维晶格上的量子多体系统，并讨论持续电流作为系统大小的函数的标度。我们表明，当守恒量由与内部对称性或哈密顿量本身相关的诺特定荷给出时，相应的持续电流可以由距离与系统大小成比例的两个算符的关联函数界定，这意味着它们至少以代数形式随系统大小增加而衰减。相比之下，偶然守恒量的持续电流即使在热力学极限下且即使存在时间反演对称性时也可以非零。我们以(S = 1/2) XXZ 自旋链中的“能量流电流”为例进行讨论，并得到持续电流的解析表达式。
