Renyi entropy of chaotic eigenstates.
Renyi entropy of chaotic eigenstates.
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混沌本征态的 Renyi 熵。
DOI：
10.1103/physreve.99.032111
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
T. Grover
中科院分区：
文献类型：
--
作者：
Tsung;T. Grover
利用建立在遍历性基础上的论据，我们推导出Renyi纠缠熵的解析表达式，我们推测它适用于混沌多体哈密顿量的有限能量密度特征态。该表达式是状态密度的普遍函数，并且即使子系统是总系统的有限部分时也是有效的——在这种情况下，简化的密度矩阵不是热的。我们发现在热力学极限下，只有von Neumann熵密度与系统总比值V_{A}/V无关，而Renyi熵密度与系统总比值V_{A}/V呈非线性关系。令人惊讶的是，n>1的Renyi熵S_{n}是子系统尺寸的凸函数，其体积律系数依赖于V_{a}/V，并且在相同能量密度下超过热混合态。我们提供了两个不同的论据来支持我们的结果：第一个依赖于混沌量子力学系统的Berry公式的多体版本，并且与本征态热化假设密切相关。第二个论点依赖于这样的假设，即对于子系统中的固定能量，能量守恒所允许的补充中的所有状态都是等可能的。我们对量子自旋链哈密顿量进行了精确对角化研究，以验证我们的分析预测。
Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies which, we conjecture, applies to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of the density of states and is valid even when the subsystem is a finite fraction of the total system-a regime in which the reduced density matrix is not thermal. We find that in the thermodynamic limit, only the von Neumann entropy density is independent of the subsystem to the total system ratio V_{A}/V, while the Renyi entropy densities depend nonlinearly on V_{A}/V. Surprisingly, Renyi entropies S_{n} for n>1 are convex functions of the subsystem size, with a volume law coefficient that depends on V_{A}/V, and exceeds that of a thermal mixed state at the same energy density. We provide two different arguments to support our results: the first one relies on a many-body version of Berry's formula for chaotic quantum-mechanical systems, and is closely related to the eigenstate thermalization hypothesis. The second argument relies on the assumption that for a fixed energy in a subsystem, all states in its complement allowed by the energy conservation are equally likely. We perform an exact diagonalization study on quantum spin-chain Hamiltonians to test our analytical predictions.