Schiro Marco, Scarlatella Orazio
JEIP, USR 3573 CNRS, Collége de France, PSL Research University, 11, place Marcelin Berthelot, 7 5231 Paris Cedex 05, France.
Institut de Physique Théorique, Université Paris Saclay, CNRS, CEA, F-91191 Gif-sur-Yvette, France.
J Chem Phys. 2019 Jul 28;151(4):044102. doi: 10.1063/1.5100157.
We develop a method to study quantum impurity models, small interacting quantum systems bilinearly coupled to an environment, in the presence of an additional Markovian quantum bath, with a generic nonlinear coupling to the impurity. We aim at computing the evolution operator of the reduced density matrix of the impurity, obtained after tracing out all the environmental degrees of freedom. First, we derive an exact real-time hybridization expansion for this quantity, which generalizes the result obtained in the absence of the additional Markovian dissipation and which could be amenable to stochastic sampling through diagrammatic Monte Carlo. Then, we obtain a Dyson equation for this quantity and we evaluate its self-energy with a resummation technique known as the noncrossing approximation. We apply this novel approach to a simple fermionic impurity coupled to a zero temperature fermionic bath and in the presence of Markovian pump, losses, and dephasing.
我们开发了一种方法来研究量子杂质模型，即在存在额外马尔可夫量子浴且与杂质具有一般非线性耦合的情况下，与环境双线性耦合的小相互作用量子系统。我们的目标是计算在剔除所有环境自由度后得到的杂质约化密度矩阵的演化算符。首先，我们为这个量推导了一个精确的实时杂化展开式，它推广了在没有额外马尔可夫耗散情况下得到的结果，并且可以通过图解蒙特卡罗方法进行随机抽样。然后，我们为这个量得到了一个戴森方程，并使用一种称为非交叉近似的重求和技术来评估其自能。我们将这种新方法应用于一个与零温费米子浴耦合且存在马尔可夫泵浦、损耗和退相的简单费米子杂质。
