论文标题
特征态热化，可观察到破坏了哈密顿对称性及其相互作用的集成系统的对应物
Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
论文作者
论文摘要
我们研究了打破自旋链哈密顿量的转化对称性的可观察到的异构矩阵元素，因此将能量特征状态连接起来，这些能量特征状态来自不同的总质子膜扇区。我们考虑了哈密顿量的量子 - 偶然和相互作用的可相互作用点，并专注于光谱中心的平均能量。在量子 - 偶然模型中，我们发现存在本征态热化。具体而言，矩阵元素是高斯分布的，其方差为$ω=e_α-e_β$（{$e_α$}的平滑函数是特征力），并且比例为$ 1/d $（$ d $是希尔伯特空间尺寸）。在相互作用的集成模型中，我们发现矩阵元素表现出偏斜的log-normal样分布，并且具有$ω$的平滑函数，该函数的缩放为$ 1/d $。我们详细研究了基质元素方差的低频行为，以揭示其表现出扩散或弹道缩放的状态。我们表明，在量子 - 偶然模型中，方差的行为在质量上相似，对于连接来自相同和不同的准膜扇区的本征态的基质元素。我们还表明，对于可观察到的可观察到的可观察到的相互作用模型并非如此，如果添加作为对哈密顿式的扰动，其翻译不变的对应物不会破坏集成性。
We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and interacting integrable points of the Hamiltonian, and focus on average energies at the center of the spectrum. In the quantum-chaotic model, we find that there is eigenstate thermalization; specifically, the matrix elements are Gaussian distributed with a variance that is a smooth function of $ω=E_α-E_β$ ({$E_α$} are the eigenenergies) and scales as $1/D$ ($D$ is the Hilbert space dimension). In the interacting integrable model, we find that the matrix elements exhibit a skewed log-normal-like distribution and have a variance that is also a smooth function of $ω$ that scales as $1/D$. We study in detail the low-frequency behavior of the variance of the matrix elements to unveil the regimes in which it exhibits diffusive or ballistic scaling. We show that in the quantum-chaotic model the behavior of the variance is qualitatively similar for matrix elements that connect eigenstates from the same versus different quasimomentum sectors. We also show that this is not the case in the interacting integrable model for observables whose translationally invariant counterpart does not break integrability if added as a perturbation to the Hamiltonian.
