Santos Lea F, Polkovnikov Anatoli, Rigol Marcos
Department of Physics, Yeshiva University, New York, New York 10016, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):010102. doi: 10.1103/PhysRevE.86.010102. Epub 2012 Jul 5.
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.
我们研究了在对多体晶格哈密顿量的本征态进行部分晶格求迹后得到的混合态的性质。对于一般系统，出现了两种情况：(i) 当对少数几个格点求迹时，对角熵变得等同于热力学熵（弱典型性）；(ii) 当对很大一部分晶格求迹时，冯·诺依曼（纠缠）熵变得等同于热力学熵（强典型性）。值得注意的是，无论对晶格的哪一部分求迹，用约化密度矩阵、对角密度矩阵和正则密度矩阵得到的少体可观测量的结果都非常相似。因此，对于这里研究的所有物理量，对角系综中的结果与热学预测相符。
