论文标题
多体局部状态中新出现的千古行为
Emerging ergodic behavior within many-body localized states
论文作者
论文摘要
我们在本文中报告了一维旋转的能级间距统计数据的数值分析-1/2 $ xxz模型，以随机的现场纵向磁场$ b_i $（$ -h \ leq b_i \ leq h $））。我们专注于强障碍限制$ j _ {\ perp} << j_z，h）$，其中$ j_z $和$ j _ {\ perp} $分别是$ z $中的（最近的邻居）旋转相互作用强度 - 和平面（$ xy $） - 指示。预计该系统将处于此参数制度中的多体局部（MBL）状态。通过分析能量水平的间距统计数据作为随机磁场强度的函数$ h $，多体状态$ e $的能量，系统中的旋转 - $ \ uparrow $粒子$ m = \ sum_i（s_i^z+{1 \ {1 \ over2}）$和$ j_z $ j_z $ j_z $ j___________当$ m \ sim {n \ over2} $（$ n = $ spin链的长度）时，区域$ j_z \ sim h $在多体能量谱的中间出现在多体能量谱的中间。与存在弱阶层极限的常规厄基阶段相比，新兴的厄贡阶段在质量上显示了质量不同的行为。
We report in this paper our numerical analysis of energy level spacing statistics for the one-dimensional spin-$1/2$ XXZ model in random on-site longitudinal magnetic fields $B_i$ ($-h\leq B_i\leq h$)). We concentrate on the strong disorder limit $J_{\perp}<<J_z,h)$ where $J_z$ and $J_{\perp}$ are the (nearest neighbor) spin interaction strength in $z$- and planar ($xy$)- directions, respectively. The system is expected to be in a many-body localized (MBL) state in this parameter regime. By analyzing the energy-level spacing statistics as a function of strength of random magnetic field $h$, energy of the many-body state $E$, the number of spin-$\uparrow$ particles in the system $M=\sum_i(s_i^z+{1\over2})$ and the spin interaction strengths $J_z$ and $J_{\perp}$, we show that there exists a small parameter region $J_z\sim h$ where ergodic behaviour emerges at the middle of the many-body energy spectrum when $M\sim{N\over2}$ ($N=$ length of spin chain). The emerging ergodic phase shows qualitatively different behaviour compared with the usual ergodic phase that exists in the weak-disorder limit.
