标题： 各种守恒量的消失和非消失持久电流 显示英文标题

标题： Vanishing and non-vanishing persistent currents of various conserved quantities

摘要： 对于每一个写成局部项之和的守恒量，都存在一个对应的电流算符，该算符满足连续性方程。 平衡状态下电流算符的期望值定义了持久电流，这些持久电流表征了系统的自发流动。 在本工作中，我们考虑有限一维晶格上的量子多体系统，并讨论持久电流随系统尺寸变化的尺度。 我们证明，当守恒量为与内部对称性相关的诺特定荷或哈密顿量本身时，对应的持久电流可以通过距离与系统尺寸成比例的两个算符的相关函数来界定，这意味着随着系统尺寸的增加，它们至少以代数方式衰减。 相反，偶然守恒量的持久电流即使在热力学极限下，甚至在时间反演对称性存在的情况下也可能不为零。 我们以$S=1/2$ XXZ 自旋链中的“能量流密度”为例进行讨论，并得到了持久电流的解析表达式。 显示英文摘要

摘要： 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 work, 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.