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arXiv 2104.03312quant-phcond-mat.dis-nncond-mat.mes-hallcond-mat.stat-mech
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耦合到有限量子浴的两态系统的部分热化

Partial thermalisation of a two-state system coupled to a finite quantum bath

Philip JD Crowley, Anushya Chandran

摘要:

本征态热化假说(ETH)是对热化量子系统中本征能、本征态和局域算符矩阵元的统计描述。我们开发了一个ETH的部分热化系统组成的自旋1/2耦合到一个有限的量子浴的类似ananterior。自旋浴耦合足够弱以至于ETH不适用,但足够强以至于微扰理论失败。我们计算了(i)保真度磁化率的分布,它采取广泛分布的形式,(ii)自旋本征态熵的分布,它采取双峰形式,(iii)自旋观测量的无限时间记忆,(iv)非高斯浴上的局部算子的矩阵元的分布,以及(v)浴的中间熵增强,其在零和$\log 2$的ETH值之间平滑地插值。这种增强是罕见的多体共振的结果,并且渐近大于典型的本征态纠缠熵。我们验证了这些结果的数值和讨论他们的连接到多体局域化过渡。

英文摘要:

The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially thermalising system composed of a spin-1/2 coupled to a finite quantum bath. The spin-bath coupling is sufficiently weak that ETH does not apply, but sufficiently strong that perturbation theory fails. We calculate (i) the distribution of fidelity susceptibilities, which takes a broadly distributed form, (ii) the distribution of spin eigenstate entropies, which takes a bi-modal form, (iii) infinite time memory of spin observables, (iv) the distribution of matrix elements of local operators on the bath, which is non-Gaussian, and (v) the intermediate entropic enhancement of the bath, which interpolates smoothly between zero and the ETH value of $\log 2$. The enhancement is a consequence of rare many-body resonances, and is asymptotically larger than the typical eigenstate entanglement entropy. We verify these results numerically and discuss their connections to the many-body localisation transition.

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