论文标题
在多体量子混乱的最小骨气模型中的光谱形态。
Spectral form factor in a minimal bosonic model of many-body quantum chaos
论文作者
论文摘要
我们研究了定期踢骨链中的光谱形式。我们考虑了一个模型家族，其中一个在Fock空间中具有对角线术语的哈密顿量，包括随机的化学势和配对相互作用，由另一位带有最近邻居的Hamiltonian定期踢出，并带有最近邻居的跳跃和配对术语。我们表明，对于中间范围的相互作用，随机相位近似可用于根据有效的玻色剂哈密顿量产生的双层多体过程来重写光谱形式。在粒子数保存的情况下，即，当不存在配对项时，有效的哈密顿量具有非亚洲$ su（1,1）$对称性，导致无效时间的通用二次缩放具有系统的大小，无论粒子数量如何。这是有效汉密尔顿二级特征值的退化对称多重组的结果，并被配对术语打破了。在后一种情况下，我们从数值上找到了无与伦比的时间尺寸依赖性，与踢式费米子链的最新研究相比。
We study spectral form factor in periodically-kicked bosonic chains. We consider a family of models where a Hamiltonian with the terms diagonal in the Fock space basis, including random chemical potentials and pair-wise interactions, is kicked periodically by another Hamiltonian with nearest-neighbor hopping and pairing terms. We show that for intermediate-range interactions, random phase approximation can be used to rewrite the spectral form factor in terms of a bi-stochastic many-body process generated by an effective bosonic Hamiltonian. In the particle-number conserving case, i.e., when pairing terms are absent, the effective Hamiltonian has a non-abelian $SU(1,1)$ symmetry, resulting in universal quadratic scaling of the Thouless time with the system size, irrespective of the particle number. This is a consequence of degenerate symmetry multiplets of the subleading eigenvalue of the effective Hamiltonian and is broken by the pairing terms. In the latter case, we numerically find a nontrivial systematic system-size dependence of the Thouless time, in contrast to a related recent study for kicked fermionic chains.
