Non-Abelian Eigenstate Thermalization Hypothesis
Non-Abelian Eigenstate Thermalization Hypothesis
复制标题
DOI：
10.1103/physrevlett.130.140402
复制
发表时间：
2023-04-06
影响因子：
8.6
通讯作者：
Halpern，Nicole Yunger
中科院分区：
文献类型：
--
作者：
Murthy，Chaitanya;Babakhani，Arman;Halpern，Nicole Yunger
本征态热化假设（ETH）解释了为什么当哈密顿量缺乏对称性时，不可积量子多体系统会在内部热化。如果哈密顿量保留一个量（“电荷”），ETH意味着在微正则子空间中的电荷扇区内的热化。但是量子系统可以有不能相互交换的电荷，因此不共享特征基；微正则子空间可能不存在。此外，哈密顿量会有简并，所以ETH不需要暗示热化。我们利用量子热力学中引入的近似微正则子空间，通过设定非阿贝尔以太坊来适应非交换电荷。以SU(2)对称性为例，应用非阿贝尔ETH计算局部算子的时间平均期望值和热期望值。我们证明，在很多情况下，平均时间会变热。然而，我们发现，在物理上合理的假设下，作为全球系统大小的函数，时间平均值收敛到热平均值的速度异常缓慢。这项工作将ETH（多体物理学的基石）扩展到非交换电荷，这是最近量子热力学中一个活跃的主题。
The eigenstate thermalization hypothesis (ETH) explains why nonintegrable quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity (“charge”), the ETH implies thermalization within a charge sector—in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing anon-Abelian ETHand invoking theapproximate microcanonical subspaceintroduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local operators’ time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.