论文标题
在多体定位过渡的所有长度尺度上，本征态杂交
Eigenstates hybridize on all length scales at the many-body localization transition
论文作者
论文摘要
相互作用的量子系统可以在足够大的疾病的存在下从千古式转变为多体局部（MBL）相。这两个阶段的动力学特性都完全不同，其特征在于哈密顿量的高度激发特征状态。每个本征态可以以系统运动的运动积分（在MBL相位）的集合上的一组量子数来表征。在这项工作中，我们研究了疾病的强度（$ w $）的疾病强度的变化。我们专注于两个“碰撞”特征状态杂交的可能性，这是它们不同的范围$ r $以及杂交强度的范围。我们发现，在MBL阶段，在$ r $ r $衰减的碰撞本征杂交的可能性为$ pr（r）\ propto \ exp \ exp [-r /η] $，长度比例$η（w）= 1 /（b \ log log log（w / w_c））$以关键障碍$ w_c $ w_c $ w_c $ w_c $ w_c $ w_c $ w_c $ w_c。这导致过渡时范围不变，表明在所有范围内形成了共鸣状态。该范围不变性无法生存到厄加德阶段，在大范围内，杂交的可能性更高，这一事实可以通过简单的组合参数来理解。实际上，对这些组合效应的补偿使我们能够在MBL阶段定义一个额外的相关长度$ξ$，这与以前的工作非常吻合，并且在过渡时期将关键值$ 1 / \ log（2）$在以前的工作中发现，以破坏MBL阶段。最后，我们表明，MBL相中的杂交中的深处是特征态在能量上接近的两级碰撞所主导的。
An interacting quantum system can transition from an ergodic to a many-body localized (MBL) phase under the presence of sufficiently large disorder. Both phases are radically different in their dynamical properties, which are characterized by highly excited eigenstates of the Hamiltonian. Each eigenstate can be characterized by the set of quantum numbers over the set of (local, in the MBL phase) integrals of motion of the system. In this work we study the evolution of the eigenstates of the disordered Heisenberg model as the disorder strength, $W$, is varied adiabatically. We focus on the probability that two `colliding' eigenstates hybridize as a function of both the range $R$ at which they differ as well as the strength of their hybridization. We find, in the MBL phase, that the probability of a colliding eigenstate hybridizing strongly at range $R$ decays as $Pr(R)\propto \exp [-R/η]$, with a length scale $η(W) = 1 / (B \log(W / W_c) )$ which diverges at the critical disorder strength $W_c$. This leads to range-invariance at the transition, suggesting the formation of resonating cat states at all ranges. This range invariance does not survive to the ergodic phase, where hybridization is exponentially more likely at large range, a fact that can be understood with simple combinatorial arguments. In fact, compensating for these combinatorial effects allows us to define an additional correlation length $ξ$ in the MBL phase which is in excellent agreement with previous works and which takes the critical value $1 / \log(2)$ at the transition, found in previous works to destabilize the MBL phase. Finally, we show that deep in the MBL phase hybridization is dominated by two-level collisions of eigenstates close in energy.
