标题： 一维系统在非零温度下费米黄金法则的分解 显示英文标题

标题： Breakdown of Fermi's Golden Rule in 1d systems at non-zero temperature

摘要： 在相互作用的量子系统中，由于准粒子的相互作用引起的退相干，单粒子格林函数预计会随时间衰减。 在弱相互作用强度（$\Delta$）的极限下，直接应用费米黄金规则（FGR）预测准粒子的衰变率为$\mathcal{O}(\Delta^{2})$。 然而，对于格点上的一维费米子在$T>0$时，此计算给出发散结果，准粒子寿命与相互作用强度的标度关系仍然是一个开放问题。 在本工作中，我们提出了解决该问题的方法：结合最近引入的耗散辅助算符演化（DAOE）方法的数值模拟，以及非微扰图解重求和，我们预测准粒子衰变率$\tau^{-1} \sim \Delta^{2} \log \Delta^{-2}$存在对数增强。 我们认为这种效应存在于各种广为人知的弱相互作用量子费米子和玻色子系统中，甚至在某些经典系统中也存在，前提是无相互作用极限下具有具有通用色散的准粒子。 显示英文摘要

摘要： In interacting quantum systems, the single-particle Green's function is expected to decay in time due to the interaction induced decoherence of quasiparticles. In the limit of weak interaction strengths ($\Delta$), a naive application of Fermi's Golden Rule (FGR) predicts an $\mathcal{O}(\Delta^{2})$ quasiparticle decay rate. However, for 1d fermions on the lattice at $T>0$, this calculation gives a divergent result and the scaling of the quasiparticle lifetime with interaction strength remains an open question. In this work we propose a solution to this question: combining numerical simulations using the recently introduced dissipation-assisted operator evolution (DAOE) method, with non-perturbative diagrammatic re-summations, we predict a logarithmic enhancement of the quasiparticle decay rate $\tau^{-1} \sim \Delta^{2} \log \Delta^{-2}$. We argue that this effect is present in a wide variety of well-known weakly interacting quantum fermionic and bosonic systems, and even in some classical systems, provided the non-interacting limit has quasiparticles with a generic dispersion.