论文标题
在动力学约束模型中的转运和Rényi熵增长之间的区别
Distinction Between Transport and Rényi Entropy Growth in Kinetically Constrained Models
论文作者
论文摘要
保护定律和相关的流体动力模式对孤立的量子系统中较高的rényi熵的生长产生了重要影响。在各种随机的统一电路和哈密顿系统中已经显示出Rényi熵的动态在存在U（1）对称性的情况下遵守$ s^{（N \ GEQ 2）}（t）\ Propto T^{1/Z} $，其中$ Z $被确定为动态实用的保守运输，以保守的运输量。但是，在这里，我们证明了这种简单的识别可能在具有动力学约束的某些量子系统中不存在。特别是，我们分别研究了具有Xnor和Fredkin约束的两种类型的U（1） - 对称量子自动机回路。我们发现，虽然两种模型中的自旋传输都是延伸的，但第二个rényi熵在Xnor模型中扩散地增长，而在弗雷德金模型中则是超级飞行的。对于具有XNOR约束的系统，由于自旋相关函数可以归因于标记粒子的新兴示踪动力学，因此会产生这种区别，而Rényi熵受到粒子的集体运输的约束。我们的结果表明，在将通用量子系统中的运输和纠缠熵动态与保护定律相关联时，必须小心。
Conservation laws and the associated hydrodynamic modes have important consequences on the growth of higher Rényi entropies in isolated quantum systems. It has been shown in various random unitary circuits and Hamiltonian systems that the dynamics of the Rényi entropies in the presence of a U(1) symmetry obey $S^{(n\geq 2)}(t) \propto t^{1/z}$, where $z$ is identified as the dynamical exponent characterizing transport of the conserved charges. Here, however, we demonstrate that this simple identification may not hold in certain quantum systems with kinetic constraints. In particular, we study two types of U(1)-symmetric quantum automaton circuits with XNOR and Fredkin constraints, respectively. We find numerically that while spin transport in both models is subdiffusive, the second Rényi entropy grows diffusively in the XNOR model, and superdiffusively in the Fredkin model. For systems with XNOR constraint, this distinction arises since the spin correlation function can be attributed to an emergent tracer dynamics of tagged particles, whereas the Rényi entropies are constrained by collective transport of the particles. Our results suggest that care must be taken when relating transport and entanglement entropy dynamics in generic quantum systems with conservation laws.
