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arXiv 2202.05217cond-mat.dis-nncond-mat.stat-mech
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跨多体局域化跃迁的初态相关动力学

Initial State Dependent Dynamics Across Many-body Localization Transition

Y. Prasad, Arti Garg

备注：
14 pages, 12 figures
发表信息：
Phys. Rev. B 105, 214202 (2022)
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摘要：

研究了一维非周期势无自旋费米子相互作用系统中多体局域化（MBL）跃迁的猝灭动力学。我们考虑了大量的初始状态，其特征在于扭结的数量，$N_{kinks}$，在密度分布。在MBL转变的离域侧，动力学随着$N_{kinks}$的增加而变得更快，使得密度不平衡中的衰减指数$γ$随着$N_{kinks}$的增加而增加。均方位移的增长指数在长时间极限内表现为幂律行为$\langle x^2(t) \rangle \sim t^β$，远大于1-扭结和其他低扭结态的指数$γ$，尽管电荷密度波态的指数为$β\sim 2γ$。随着无序强度在某些临界无序下增加$γ_{N_{kink}} \rightarrow 0$，$h_{N_{kinks}}$是$N_{kinks}$的单调递增函数。一个1-扭结状态总是低估的MBL转变发生时的无序值，但$h_{1-kink}$与MBL相之前的亚扩散相的开始相一致。这与1-扭结态的界面加宽的动力学是一致的。我们发现，二分纠缠熵有对数增长$a \ln(Vt)$不仅在MBL阶段，而且在离域阶段和在这两个阶段的系数$a$增加与$N_{kinks}$以及与相互作用强度$V$。我们解释这种依赖动力学的扭结的数量在相互作用的哈密顿量的本征基的初始状态的归一化参与比。

英文摘要：

We investigate quench dynamics across many-body localization (MBL) transition in an interacting one dimensional system of spinless fermions with aperiodic potential. We consider a large number of initial states characterized by the number of kinks, $N_{kinks}$, in the density profile. On the delocalized side of the MBL transition the dynamics becomes faster with increase in $N_{kinks}$ such that the decay exponent, $γ$, in the density imbalance increases with increase in $N_{kinks}$. The growth exponent of the mean square displacement which shows a power-law behaviour $\langle x^2(t) \rangle \sim t^β$ in the long time limit is much larger than the exponent $γ$ for 1-kink and other low kink states though $β\sim 2γ$ for a charge density wave state. As the disorder strength increases $γ_{N_{kink}} \rightarrow 0$ at some critical disorder, $h_{N_{kinks}}$ which is a monotonically increasing function of $N_{kinks}$. A 1-kink state always underestimates the value of disorder at which the MBL transition takes place but $h_{1-kink}$ coincides with the onset of the sub-diffusive phase preceding the MBL phase. This is consistent with the dynamics of interface broadening for the 1-kink state. We show that the bipartite entanglement entropy has a logarithmic growth $a \ln(Vt)$ not only in the MBL phase but also in the delocalised phase and in both the phases the coefficient $a$ increases with $N_{kinks}$ as well as with the interaction strength $V$. We explain this dependence of dynamics on the number of kinks in terms of the normalized participation ratio of initial states in the eigenbasis of the interacting Hamiltonian.

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