论文标题
在具有准周期电势的一维平坦带晶格中的临界区域的拟议实现
Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
论文作者
论文摘要
在先前的工作中，已经建立了广义的Aubry-André模型（Ganeshan-Pixley-Das Sarma的模型）中关键区域的概念。在这项工作中，我们建议可以在具有准周期潜力的一维平坦带晶格系统中实现关键区域。发现上述平坦频带晶格模型可以简化为有效的Ganeshan-Pixley-Das Sarma的模型，其中有效参数$α= v_0/（2e）$具有潜在强度$ v_0 $和eigenenergy $ e $。结果表明，该模型中有非常丰富的物理学。取决于$ |α| <1 $或$ |α| \ geq1 $，有效的准周期电位将被界定或无限。在这两种情况下，局部长度的Lyapunov指数[$γ（E）$]，移动性边缘（$ e_c $）和关键索引（$ν$）。此外，在参数$ v_0-e $平面中将出现几个局部状态区域，扩展州区域和关键区域。对于给定的潜在强度$ v_0 $，本地化扩展和局部临界过渡可以共存。此外，我们发现局部长度$ξ（e）= 1/γ（e）的关键索引是$ν= 1 $附近的局部扩展过渡和$ν= 1/2 $附近的局部临界过渡。接近绑定（$ |α| <1 $）与无界（$ | |α| \ geq1 $）案例之间的过渡点，即$ |α| = | v_0/（2e）| = 1 $，局部态度的lypunov指数的衍生物是不连续的。可以通过Avila的加速度来区分有限和无限案例中的本地化状态。最后，我们发现在过渡点附近，相图中也存在关键的扩展过渡。
In the previous work, the concept of critical region in a generalized Aubry-André model (Ganeshan-Pixley-Das Sarma's model) has been set up. In this work we propose that the critical region can be realized in a one-dimensional flat band lattice system with a quasi-periodic potential. It is found that the above flat band lattice model can be reduced into an effective Ganeshan-Pixley-Das Sarma's model where the effective parameter $α=V_0/(2E)$ with potential strength $V_0$ and eigenenergy $E$. It is shown that there are very rich physics in this model. Depending on $|α|<1$ or $|α|\geq1$, the effective quasi-periodic potential would be bounded or unbounded. For these two cases, the Lyapunov exponent [$γ(E)$], mobility edges ($E_c$) and critical indices ($ν$) of localized length are obtained exactly. In addition, several localized state regions, extended state regions and critical regions would appear in the parameter $V_0-E$ plane. For a given potential strength $V_0$, the localized-extended and localized-critical transitions can co-exist. Furthermore, we find the critical index of localized length $ξ(E)=1/γ(E)$ is $ν=1$ near localized-extended transitions and $ν=1/2$ near the localized-critical transitions. Near the transition point between the bound ($|α|<1$) and unbounded ($|α|\geq1$) cases, i.e, $|α|=|V_0/(2E)|= 1$, the derivative of Lypunov exponent of localized states with respect to energy is discontinuous. The localized states in bounded and unbounded cases can be distinguished from each other by Avila's acceleration. At the end, we find that near the transition point, there also exist critical-extended transitions in the phase diagram.
