Decoherence and Relaxation in Quantum Spin Clusters

主要目的是阐明单位时间演化下的少体自旋系统的内部退相干。这里退相干指的是子系统的行为。Schnack小组：我们感兴趣的是内部退相干减少的情况，类似于通过多体局域化等现象阻止弛豫和热化的方案。我们计划进一步研究守恒定律的作用，减少环面力矩系统退相干的可能性，以及特定外部驱动对退相干自旋系统重新聚焦的影响。我们还希望将研究系统的范围从纯自旋系统扩展到自旋声子系统。Michielsen小组：由于量子操作不再是一个未来的梦想，而是在我们今天的手中，我们提出了一个应用，用量子退火器模拟哈伯德模型的基态能量的计算。为了考虑退相干的环境自旋，我们将根据时变薛定谔方程，通过对组合系统进行时间演化，研究嵌入自旋池中的Hubbard模型。这两位博士生将在数值方法和物理概念上进行强烈的互动。目标A：驱动动力学以提高相干性：我们想研究周期性或非周期性刺激/驱动系统和/或系统如何引起系统的退相干。这尤其涉及多自旋系统的自由感应衰变的模拟，以及它们在哈恩回波和一般乌里格脉冲序列存在下的研究。目标B：环面矩的退相干和弛豫：像时钟跃迁一样，具有明显环面矩的态的叠加可能对其他自旋或波动磁场的磁干扰更强。目标C：自旋-声子系统中的退相干：我们现在可以研究自旋和声子的组合系统，这一扩展为磁稀释化合物提供了非常现实的描述。它将允许在声子子系统引起的避平交叉处研究所谓的内摩擦。目标D：量子退火的哈伯德模型的重新表述：使用Jordan-Wigner变换，一维哈伯德模型可以被表述为一个2n -量子位模型，该模型定义在一个两条腿的阶梯上，其中阶梯的第一（第二）腿上的量子位对应于自旋向上（自旋向下）的费米子。我们计划利用大规模并行量子自旋动力学模拟器模拟理想的模拟量子退火过程，研究各种填充的18x1和3x6 Hubbard模型（对应36量子位模型）的基态能量。目标E: Hubbard模型的研究：我们提出研究环境温度和无序度对理想量子退火的影响。因此，我们通过求解整个系统的时变薛定谔方程来模拟与热浴耦合的量子曼尼尔。

The major goal is to elucidate internal decoherence in few-body spin systems under unitary time-evolution. Here decoherence refers to the behavior of asubsystem.Group Schnack: We are interested in caseswhere internal decoherence is reduced similar to schemes whererelaxation and thermalization are prevented by phenomena such asmany-body localization. We plan to further investigatethe role of conservation laws, the possibility to reducedecoherence in systems of toroidal moments and the influence ofparticular external drives to refocus decohering spin systems.We also want to extend the range of investigated systems frompure spin systems to spin-phonon systems.Group Michielsen: Since quantum manipulationis no longer a future dream, but at our hands today, we propose as an application to simulatethe calculation of the ground-state energy of the Hubbard modelwith a quantum annealer. In order to take account of decoheringenvironmental spins we will study the Hubbard model embeddedinto a bath of spins by time-evolving the combined systemaccording to the time-dependent Schroedinger equation.The two Ph.D. students will interact strongly both on numericalmethods as well as on physical concepts. Goal A: Driven dynamics to improve coherence:We want to investigate the question how periodic or aperiodic stimuli/driving of system and/or bathreduces decoherence of the system. This concerns in particularthe simulation of the free-induction decay of multi-spin systemsas well as their study in the presence of Hahn echos and generalUhrig pulse sequences.Goal B: Decoherence and relaxation of toroidal moments:Like clock transitions,superpositions of states with pronounced toroidal moments may bemore robust against magnetic disturbances by other spins orfluctuating magnetic fields. Goal C: Decoherence in spin-phonon systems:We can now investigate combined systems of spins and phonons, an extension that offers veryrealistic descriptions for magnetically diluted compounds. Itwould allow to study so-called internal friction at avoidedlevel crossings induced by the phonon subsystem.Goal D: Reformulation of the Hubbard model for quantum annealing:Using the Jordan-Wigner transformation, the one-dimensionalHubbard model can be formulated as a 2N-qubit modeldefined on a two-leg ladder where the qubits on the first(second) leg of the ladder correspond to the spin-up (spin-down)fermions. We plan to study the ground state energy of the18x1 and 3x6 Hubbard model, corresponding to a36-qubit model, for various fillings by simulating the ideal analog quantumannealing process by using the Massively Parallel Quantum SpinDynamics Simulator.Goal E: Investigation of the Hubbard model:We propose to study theeffect of the environmental temperature and disorder on idealquantum annealing. We therefore simulate the quantumannealer coupled to a heat bath by solving the time-dependentSchroedinger equation of the whole system.