耗散量子自旋系统中两时间关联的演化：老化和等级动力学
Evolution of two-time correlations in dissipative quantum spin systems: aging and hierarchical dynamics
摘要：
我们考虑了量子XXZ自旋链中两次关联的演化，它与引起退相的环境相接触。扩展准精确含时矩阵乘积态技术考虑耗散系统内的两次相关的动力学，我们揭示了这些相关性沿所有自旋方向的完整量子行为。再加上绝热消除和动力学蒙特卡罗的见解，我们确定了三个动力学制度。对于初始时刻，它们的演化受系统幺正动力学控制，并依赖于初始状态和哈密顿参数。对于弱自旋-自旋相互作用各向异性，在此初始动力学制度之后，两次相关性进入代数标度制度，这标志着时间平移不变性的崩溃和老化的出现。对于较强的相互作用各向异性，这些相关性首先通过拉伸指数制度，然后进入代数。这种复杂的弛豫是由于能量昂贵的激发的扩散动力学与它们的运动之间的竞争而产生的。因此，自旋系统的耗散加热动力学可以用来探测整个频谱的基础哈密顿量。
英文摘要：
We consider the evolution of two-time correlations in the quantum XXZ spin-chain in contact with an environment causing dephasing. Extending quasi-exact time-dependent matrix product state techniques to consider the dynamics of two-time correlations within dissipative systems, we uncover the full quantum behavior for these correlations along all spin directions. Together with insights from adiabatic elimination and kinetic Monte Carlo, we identify three dynamical regimes. For initial times, their evolution is dominated by the system unitary dynamics and depends on the initial state and the Hamiltonian parameters. For weak spin-spin interaction anisotropy, after this initial dynamical regime, two-time correlations enter an algebraic scaling regime signaling the breakdown of time-translation invariance and the emergence of aging. For stronger interaction anisotropy, these correlations first go through a stretched exponential regime before entering the algebraic one. Such complex relaxation arises due to the competition between the proliferation dynamics of energetically costly excitations and their motion. As a result, dissipative heating dynamics of spin systems can be used to probe the entire spectrum of the underlying Hamiltonian.
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