Ślusarski Tomasz, Wrześniewski Kacper, Weymann Ireneusz
Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznańskiego 2, Poznań, 61-614, Poland.
Sci Rep. 2022 Jun 13;12(1):9799. doi: 10.1038/s41598-022-14108-x.
We study the dynamical properties of the one-channel and two-channel spin-1/2 Kondo models after quenching in Hamiltonian variables. Eigen spectrum of the initial and final Hamiltonians is calculated by using the numerical renormalization group method implemented within the matrix product states formalism. We consider multiple quench protocols in the considered Kondo systems, also in the presence of external magnetic field of different intensities. The main emphasis is put on the analysis of the behavior of the Loschmidt echo L(t), which measures the ability of the system's revival to its initial state after a quench. We show that the decay of the Loschmidt echo strongly depends on the type of quench and the ground state of the system. For the one-channel Kondo model, we show that L(t) decays as, [Formula: see text], where [Formula: see text] is the Kondo temperature, while for the two-channel Kondo model, we demonstrate that the decay is slower and given by [Formula: see text]. In addition, we also determine the dynamical behavior of the impurity's magnetization, which sheds light on identification of the relevant time scales in the system's dynamics.
我们研究了哈密顿量变量猝灭后单通道和双通道自旋-1/2近藤模型的动力学性质。通过使用在矩阵乘积态形式体系内实现的数值重整化群方法来计算初始和最终哈密顿量的本征谱。我们考虑了所研究的近藤系统中的多种猝灭协议，也考虑了不同强度外磁场存在的情况。主要重点在于对洛施密特回波(L(t))行为的分析，它衡量了系统在猝灭后恢复到初始状态的能力。我们表明，洛施密特回波的衰减强烈依赖于猝灭类型和系统的基态。对于单通道近藤模型，我们表明(L(t))按([公式：见正文])衰减，其中([公式：见正文])是近藤温度，而对于双通道近藤模型，我们证明衰减较慢，由([公式：见正文])给出。此外，我们还确定了杂质磁化的动力学行为，这有助于揭示系统动力学中相关时间尺度的识别。
