论文标题
偏离最大纠缠的中谱特征状态的最大纠缠
Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians
论文作者
论文摘要
在由当地哈密顿量管理的自旋链中，我们考虑了能量光谱中间的微型典型集合和一个连续的子系统，其长度是系统大小的恒定分数。我们证明，如果集合的带宽大于一定常数，则在集合中的特征状态的平均纠缠熵（在子系统和系统的其余部分之间）至少具有正常常数。该结果突出了（混乱的）汉密尔顿人和随机状态的中谱特征状态和随机状态的纠缠熵之间的差异。我们还证明，前者以相同的能量偏离热力学熵的偏离至少一个正常数。
In a spin chain governed by a local Hamiltonian, we consider a microcanonical ensemble in the middle of the energy spectrum and a contiguous subsystem whose length is a constant fraction of the system size. We prove that if the bandwidth of the ensemble is greater than a certain constant, then the average entanglement entropy (between the subsystem and the rest of the system) of eigenstates in the ensemble deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of (chaotic) local Hamiltonians and that of random states. We also prove that the former deviates from the thermodynamic entropy at the same energy by at least a positive constant.
