Vidmar Lev, Rigol Marcos
Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Phys Rev Lett. 2017 Dec 1;119(22):220603. doi: 10.1103/PhysRevLett.119.220603. Epub 2017 Nov 29.
In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the average entanglement entropy is known to be nearly maximal, with a deviation that is, at most, a constant. Here we prove that, in a system that is away from half filling and divided in two equal halves, an upper bound for the average entanglement entropy of random pure states with a fixed particle number and normally distributed real coefficients exhibits a deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.
在量子统计力学中，理解量子混沌哈密顿量本征态的二分纠缠熵与最大值有多接近是具有根本重要性的。对于希尔伯特空间中的随机纯态，已知平均纠缠熵几乎是最大的，其偏差至多为一个常数。在这里我们证明，在一个远离半填充且被分成两个相等部分的系统中，具有固定粒子数且实系数呈正态分布的随机纯态的平均纠缠熵的上限与最大值的偏差会随着系统体积的平方根增长。一个粒子数守恒量子混沌模型的高激发本征态的精确数值结果表明，随着系统尺寸增加，该界限会达到饱和。
