论文标题
通过量子复杂性探测量子疤痕和弱牙
Probing quantum scars and weak ergodicity-breaking through quantum complexity
论文作者
论文摘要
疤痕状态是特殊的多体征态，违反了本征态热假说（ETH）。我们使用兰开斯算法的显式形式主义，通常称为在这种情况下的正向散射近似，我们计算了由PXP汉密尔顿的时间演化产生的典型状态的Krylov状态（扩散）复杂性，并托有此类状态。我们表明，Neel状态的复杂性近似地恢复了，而通用伦理的复杂性总是在增加。这可以归因于哈密顿量相应发生器的近似SU（2）结构。我们通过Q构造的SU（2）代数量化了这种“亲密关系”，并为近似Krylov子空间内的Neel状态提供了兰开斯系数的分析表达。我们用紧密结合模型直观地解释结果。我们进一步考虑了PXP哈密顿量的变形，并计算相应的Lanczos系数和复杂性。我们发现，Neel状态的复杂性几乎显示出完美的复兴，而对于通用的伦理学状态并不成立。
Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using the explicit formalism of the Lanczos algorithm, usually known as the forward scattering approximation in this context, we compute the Krylov state (spread) complexity of typical states generated by the time evolution of the PXP Hamiltonian, hosting such states. We show that the complexity for the Neel state revives in an approximate sense, while complexity for the generic ETH-obeying state always increases. This can be attributed to the approximate SU(2) structure of the corresponding generators of the Hamiltonian. We quantify such ''closeness'' by the q-deformed SU(2) algebra and provide an analytic expression of Lanczos coefficients for the Neel state within the approximate Krylov subspace. We intuitively explain the results in terms of a tight-binding model. We further consider a deformation of the PXP Hamiltonian and compute the corresponding Lanczos coefficients and the complexity. We find that complexity for the Neel state shows nearly perfect revival while the same does not hold for a generic ETH-obeying state.
