高斯态中的保持对称性的二次Lindbladian与耗散驱动的拓扑转变
Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States
AI总结：
本文提出通过模哈密顿量的拓扑不变量表征开放量子系统密度矩阵拓扑，推导了费米子高斯态下保持对称性的Lindbladian算符条件，并展示了耗散驱动的有限时间拓扑转变及物理特征。
AI中文摘要：
开放量子系统的动力学演化可以由密度矩阵的Lindblad方程来支配。在本文中，我们提出通过其模哈密顿量的拓扑不变量来表征密度矩阵拓扑。由于此类哈密顿量的拓扑分类取决于它们的对称类，我们解决的一个主要问题是确定Lindbladian算符的要求，使得模哈密顿量在动力学演化过程中能够保持其对称类。我们针对费米子高斯态以及作为一组费米子算符的二次算符的模哈密顿量解决了这个问题。当这些条件得到满足，并且模哈密顿量对称类具有非平凡的拓扑分类时，随着时间演化可能会发生拓扑转变。我们展示了耗散驱动拓扑转变的两个例子，其中模哈密顿量分别属于具有U(1)对称性的AIII类和不具有U(1)对称性的DIII类。通过有限尺寸标度分析，我们表明该密度矩阵拓扑转变发生在有限时间内。我们还展示了该转变的物理特征。
英文摘要：
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution. We solve this problem for the fermionic Gaussian state and for the modular Hamiltonian being a quadratic operator of a set of fermionic operators. When these conditions are satisfied, along with a nontrivial topological classification of the symmetry class of the modular Hamiltonian, a topological transition can occur as time evolves. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class with U(1) symmetry and the DIII class without U(1) symmetry. By a finite size scaling, we show that this density matrix topology transition occurs at a finite time. We also present the physical signature of this transition.
