Fermionic superoperators for zero-temperature nonlinear transport: Real-time perturbation theory and renormalization group for Anderson quantum dots
Fermionic superoperators for zero-temperature nonlinear transport: Real-time perturbation theory and renormalization group for Anderson quantum dots
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DOI：
10.1103/physrevb.86.235432
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发表时间：
2012-07
影响因子：
3.7
通讯作者：
R. B. Saptsov;M. Wegewijs
中科院分区：
文献类型：
--
作者：
R. B. Saptsov;M. Wegewijs
本文利用实时重整化群（RT-RG）在约化密度算子的动力学方程框架下研究了零温度下强相互作用Anderson量子点的输运。通过引入符合费米子统计量的场超算子，进一步发展了一般有限温度实时输运形式。这种在Liouville-Fock空间中的直接二次量化极大地简化了在anderson模型对称变换下不可约变换的算子和超算子的构造。费米子场超算符自然地产生于整个系统的单价（费米-宇称）超选择规则。用这些场超算子表示，有效时间演化超算子核的微扰理论的因果结构变得明确。因果结构也暗示了一个费米子宇称保护特征向量的存在，解释了最近报道的绝热驱动结果[物理学]。并将其推广到隧道耦合中的任意阶。此外，在WBL中，因果表示以指数方式减少了时间演化核图的数量。我们在有限电压和磁场下进行了完整的2环RG分析，同时系统地考虑了对量子点和储层频率的依赖。利用liouville空间中的二次量化和对称限制，我们得到了具有有效数值解的解析RT-RG方程，并对模型参数空间进行了广泛的研究，不包括Kondo区域。合并重整化效应导致非弹性共隧峰的增强。此外，我们发现在有限电压下，无论是在SET还是ICT状态下，稳定性图都存在隧道诱导的非线性。
We study the transport through a strongly interacting Anderson quantum dot at zero-temperature using the real-time renormalization group (RT-RG) in the framework of a kinetic equation for the reduced density operator. We further develop the general finite temperature real-time transport formalism by introducing field superoperators that obey fermionic statistics. This direct second quantization in Liouville-Fock space strongly simplifies the construction of operators and superoperators which transform irreducibly under the Anderson-model symmetry transformations. The fermionic field superoperators naturally arise from the univalence (fermion-parity) superselection rule for the total system. Expressed in these field superoperators, the causal structure of the perturbation theory for the effective time-evolution superoperator-kernel becomes explicit. The causal structure also implies the existence of a fermion-parity protected eigenvector of the exact Liouvillian, explaining a recently reported result on adiabatic driving [Phys. Rev. B 85, 075301 (2012)] and generalizing it to arbitrary order in the tunnel coupling. Furthermore, in the WBL the causal representation exponentially reduces the number of diagrams for the time-evolution kernel. We perform a complete 2-loop RG analysis at finite voltage and magnetic field, while systematically accounting for the dependence on both the quantum dot and reservoir frequencies. Using the second quantization in Liouville-space and symmetry restrictions we obtain analytical RT-RG equations with an efficient numerical solution and we extensively study the model parameter space, excluding the Kondo regime. The incorporated renormalization effects result in an enhancement of the inelastic cotunneling peak. Moreover, we find a tunnel-induced non-linearity of the stability diagrams at finite voltage, both in the SET and ICT regime.