发表机构
Institut für Theoretische Physik, Georg-August-Universität Göttingen; Department of Physics, The Pennsylvania State University（哥廷根大学理论物理研究所; 宾夕法尼亚州立大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过精确对角化比较量子自旋梯子中ETH谱函数的低频平台与随机矩阵及传输频率，发现传输频率系统性偏大，需深入理解差异起源。
AI 中文摘要
一般孤立多体量子系统热化的现象可通过本征态热化假说（ETH）来理解。近年来，ETH谱函数的行为引起了广泛关注，该函数描述了可观测量非对角矩阵元方差对相关能量和频率的平滑依赖，其低频部分包含关于长时间动力学的信息。在由ETH描述的有限系统中，谱函数预期在特征频率$\omega^{}_{\mathrm{ETH}}$以下呈现平台。在此区域中，可观测量矩阵元的统计预期由随机矩阵理论描述。文献中已研究的相关频率包括$\omega^{}_{\mathrm{SFF}}$（控制谱形状因子中随机矩阵行为的起始）以及传输频率$\omega^{}_{\mathrm{tr}}$（由传输系数导出）。然而，这些频率的直接定量比较尚缺乏。利用精确对角化，我们对具有扩散能量和自旋传输的干净及无序量子自旋梯子中电流算符的谱函数进行了此类比较。我们找到了ETH谱函数中预期低频平台的清晰证据。对于可访问的系统尺寸，$\omega^{}_{\mathrm{SFF}}$与平台范围一致，而传输频率则系统性更大，且位于谱函数的非普适区域。我们的发现强调了更好地理解这些定量差异起源的必要性。
英文摘要
The fact that generic isolated many-body quantum systems thermalize is understood using the eigenstate thermalization hypothesis (ETH). In recent years, there has been much interest in the behavior of the ETH spectral functions, which characterize the smooth dependence of the variance of the off-diagonal matrix elements of observables on the associated energy and frequency, and whose low-frequency part contains information about the long-time dynamics. In finite systems described by the ETH, the spectral functions are expected to exhibit plateaus below a characteristic frequency $ω^{}_{\mathrm{ETH}}$. In this regime, the statistics of the matrix elements of observables are expected to be described by random matrix theory. Related frequencies that have been studied in the literature are $ω^{}_{\mathrm{SFF}}$, which controls the onset of random-matrix behavior in the spectral form factor, and the transport frequencies $ω^{}_{\mathrm{tr}}$, which are derived from transport coefficients. However, a direct quantitative comparison of these frequencies is lacking. Using exact diagonalization, we conduct such a comparison for the spectral functions of current operators in clean and disordered quantum spin ladders with diffusive energy and spin transport. We find clear evidence for the expected low-frequency plateaus in the ETH spectral functions. For the accessible system sizes, $ω^{}_{\mathrm{SFF}}$ is consistent with the extent of the plateaus, while the transport frequencies are systematically larger and lie in the nonuniversal regime of the spectral functions. Our findings highlight the need to better understand the origin of these quantitative differences.
Comments13 pages, 9 figures
