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arXiv 1603.01293quant-ph
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热助隧穿的标度分析和瞬子及量子蒙特卡罗模拟

Scaling analysis and instantons for thermally-assisted tunneling and Quantum Monte Carlo simulations

Zhang Jiang, Vadim N. Smelyanskiy, Sergei V. Isakov, Sergio Boixo, Guglielmo Mazzola, Matthias Troyer, Hartmut Neven

备注：
15 pages, 4 figures, 45 references
发表信息：
Phys. Rev. A 95, 012322 (2017)
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摘要：

我们发展了一种瞬子演算方法，导出了全连通量子自旋模型中亚稳态的热助隧穿衰变率的解析表达式。隧穿衰变问题可以映射为经典随机动力场的Kramers逃逸问题。利用路径积分量子蒙特卡罗（QMC）方法有效地模拟了该动力学场。我们分析表明，指数标度的自旋数的热辅助量子隧穿率和逃逸率的QMC过程是相同的。我们将这种效应与瞬子隧穿通道的存在联系起来，瞬子的隧穿通道由单格点磁化矢量的非线性动力学平均场论方程描述，并精确求解。最后，我们推导出“尖刺”的障碍形状时，自旋隧道和QMC率的规模与自旋$N$的数量多项式，而一个纯粹的经典的过势垒激活率的规模指数与$N$的标度关系。

英文摘要：

We develop an instantonic calculus to derive an analytical expression for the thermally-assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path integral Quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the "spiky" barrier shape when the spin tunnelling and QMC rates scale polynomially with the number of spins $N$ while a purely classical over-the-barrier activation rate scales exponentially with $N$.

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