量子系统中的弱典型性和强典型性
Weak and strong typicality in quantum systems
摘要：
研究了由多体格点哈密顿量的本征态在追踪部分格点后得到的混合态的性质。对于一般系统，出现了两种情况：（i）当追踪到几个位置时，对角熵等价于热力学熵（弱典型性）;（ii）当追踪到大部分晶格时，冯·诺依曼（纠缠）熵等价于热力学熵（强典型性）。值得注意的是，用约化的、对角的和正则的密度矩阵得到的少体观测量的结果彼此非常相似，不管追踪到晶格的哪一部分。因此，对于这里研究的所有物理量，对角系综中的结果与热预测相匹配。
英文摘要：
We study the properties of mixed states obtained from eigenstates of many-body lattice Hamiltonians after tracing out part of the lattice. Two scenarios emerge for generic systems: (i) the diagonal entropy becomes equivalent to the thermodynamic entropy when a few sites are traced out (weak typicality); and (ii) the von Neumann (entanglement) entropy becomes equivalent to the thermodynamic entropy when a large fraction of the lattice is traced out (strong typicality). Remarkably, the results for few-body observables obtained with the reduced, diagonal, and canonical density matrices are very similar to each other, no matter which fraction of the lattice is traced out. Hence, for all physical quantities studied here, the results in the diagonal ensemble match the thermal predictions.
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