Titum Paraj, Quito Victor L, Syzranov Sergey V
Joint Quantum Institute, NIST/University of Maryland, College Park, MD 20742, USA.
National Magnetic Field Laboratory, Tallahassee, FL 32310, USA.
Phys Rev B. 2018 Jul;98(1). doi: 10.1103/physrevb.98.014201.
Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by for small frequencies and for large frequencies , where is the characteristic matrix element of excitation hopping in a system of volume , and , and are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.
受无序电子材料中的中性激发以及具有长程相互作用的捕获超冷粒子系统的启发，我们研究了在强随机势中具有幂律跳跃哈密顿量的准粒子的能级统计。在固态系统中，以中性偶极激发为代表的此类准粒子会导致局部可观测量的长程关联，并且可能主导能量传输。聚焦于无序电子系统中的激发，我们在足够强的无序极限下计算有限系统中的能级关联函数。在小能量差时，关联呈现维格纳 - 戴森统计。特别地，在非常强的无序极限下，能级关联函数对于小频率由 给出，对于大频率由 给出，其中 是体积为 的系统中激发跳跃的特征矩阵元，并且 、 和 是量级为 1 的系数，它们取决于系统的形状。我们所研究的能级关联函数允许进行直接的实验观测，例如，通过测量系统在不同频率下的交流电导的关联。
