论文标题
精确的溶液在1D Fracton系统中填充诱导的热化过渡
Exact solution for the filling-induced thermalization transition in a 1D fracton system
论文作者
论文摘要
我们研究了受约束的分裂动力学的随机电路模型，其中一维晶格上的颗粒经历了随机的局部运动。该系统的配置空间表现出弱碎片（“热化”）相之间的连续相变，并且是粒子数量密度的函数。在这里，通过映射组合学中的两个不同问题，我们确定了关键密度$ n_c $的精确解决方案。具体而言，当运营商在$ \ ell $连续站点上行动的操作员进行进化时，关键密度由$ n_c = 1/（\ ell -2）$给出。我们确定过渡附近的临界缩放，并表明相关长度指数$ν= 2 $的通用值。我们通过数字模拟确认我们的理论结果。在热化阶段，动态指数是宽度的：$ z = 4 $，而在关键点，它增加到$ z_c \ gtrsim 6 $。
We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system exhibits a continuous phase transition between a weakly fragmented ("thermalizing") phase and a strongly fragmented ("nonthermalizing") phase as a function of the number density of particles. Here, by mapping to two different problems in combinatorics, we identify an exact solution for the critical density $n_c$. Specifically, when evolution proceeds by operators that act on $\ell$ contiguous sites, the critical density is given by $n_c = 1/(\ell -2)$. We identify the critical scaling near the transition, and we show that there is a universal value of the correlation length exponent $ν= 2$. We confirm our theoretical results with numeric simulations. In the thermalizing phase the dynamical exponent is subdiffusive: $z=4$, while at the critical point it increases to $z_c \gtrsim 6$.
