论文标题
随机矩阵光谱形式在踢相互作用的费米子链中
Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains
论文作者
论文摘要
我们在存在和不存在粒子数（$ u（1）$）对称性的情况下，在定期驱动的（floquet）费米子链中研究量子混乱和光谱相关性。我们在分析上表明，光谱形式的进攻精确地遵循了长链状态中随机矩阵理论的预测，对于超过所谓的$ l $ as $ {\ cal o}（\ cal o}（\ cal o}（l^2）$的$ l $ a $ l $ a y limeless th thouble/ehrenfest的时间，$} $，或$ o {$ cal o}（\ cal o}（l^0）（l^0）（l^0）（l^0）（l^0）， 分别。使用从本质上需要远程交互本质性质的随机相假设，我们证明了您的时间缩放等同于经典马尔可夫链的光谱间隙的行为，该频谱差距分别在连续的时间（trotter）极限中，分别由Gapless $ xxx $或gapped $ xxz $ xxz $ xxz $ xxz $ xxz $ xxz $ xxz $，spin-1/2 Chain hamililton。
We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle number conservation ($U(1)$) symmetry. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains, and for timescales that exceed the so-called Thouless/Ehrenfest time which scales with the size $L$ as ${\cal O}(L^2)$, or ${\cal O}(L^0)$, in the presence, or absence of $U(1)$ symmetry, respectively. Using random phase assumption which essentially requires long-range nature of interaction, we demonstrate that the Thouless time scaling is equivalent to the behavior of the spectral gap of a classical Markov chain, which is in the continuous-time (Trotter) limit generated, respectively, by a gapless $XXX$, or gapped $XXZ$, spin-1/2 chain Hamiltonian.
