论文标题
在存在随机长期相互作用的情况下
Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions
论文作者
论文摘要
我们研究了一个无旋转费用系统中的多体定位（MBL），在存在长期相互作用的情况下，具有确定性的性质潜力，因为长期相互作用衰减，作为powerlaw $ v_ {ij}/（r_i-r_j}/（r_i-r_j）^α$，与距离且随机系数$ v_ {ij {ij} $。我们证明，MBL即使以$α<1 $的价格生存，并且在一个广泛的非共性次级阶段之前。从短距离相互作用系统显示无限温度MBL相的参数开始，打开随机幂律相互作用会导致频谱中的多体迁移率边缘，而较小的$α$值的Ergodic Delacalized状态较大。因此，关键障碍$ h_c^r $，随着相互作用的范围，非共性过渡到非共性过渡的发生。密度不平衡$ i（t）$的时间演变，它具有幂律衰减$ i（t）\ sim t^{ - γ} $在中间至较大的时间制度中，表明关键障碍$ h_ {c}^i $，上面是$γ\ sim 0 $ n $ y $ y $ mm $ h_c^yes themect in Systems digfusion-digfusion-digfusion-nep n $ mm $ hem。在$ h_ {c}^r $和$ h_ {c}^i $之间，有一个广泛的非共性亚延伸阶段，其特征在于，该阶段的特征是高度间距比，多重型特征函数和非零动力学指数$ qub $γ\ ll 1/2 $。即使在MBL过渡的梯形侧（$ h <h_c^r $），该系统仍然是不足的。对于$ h <h_ {0} <h_c^r $，该系统具有$γ> 1/2 $的超扩散。此处获得的丰富相图是远程相互作用的随机性质所独有的。我们用随机幂律相互作用引起的有效安德森模型的局部能量之间的增强相关性来解释这一点。
We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions decaying as power-law $V_{ij}/(r_i-r_j)^α$ with distance and having random coefficients $V_{ij}$. We demonstrate that MBL survives even for $α<1$ and is preceded by a broad non-ergodic sub-diffusive phase. Starting from parameters at which the short-range interacting system shows infinite temperature MBL phase, turning on random power-law interactions results in many-body mobility edges in the spectrum with a larger fraction of ergodic delocalized states for smaller values of $α$. Hence, the critical disorder $h_c^r$, at which ergodic to non-ergodic transition takes place increases with the range of interactions. Time evolution of the density imbalance $I(t)$, which has power-law decay $I(t) \sim t^{-γ}$ in the intermediate to large time regime, shows that the critical disorder $h_{c}^I$, above which the system becomes diffusion-less (with $γ\sim 0$) and transits into the MBL phase is much larger than $h_c^r$. In between $h_{c}^r$ and $h_{c}^I$ there is a broad non-ergodic sub-diffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions and a non zero dynamical exponent $γ\ll 1/2$. The system continues to be sub-diffusive even on the ergodic side ($h < h_c^r$) of the MBL transition, where the eigenstates near the mobility edges are multifractal. For $h < h_{0}<h_c^r$, the system is super-diffusive with $γ>1/2$. The rich phase diagram obtained here is unique to random nature of long-range interactions. We explain this in terms of the enhanced correlations among local energies of the effective Anderson model induced by random power-law interactions.
