论文标题
二次开放量子多体系统的临界性和相分类
Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems
论文作者
论文摘要
我们研究了由Lindblad Master方程支配的翻译不变的开放量子多体系统的稳态状态，其中Hamiltonian在梯子操作员中是二次的，而Lindblad操作员则是线性的，要么是二次的和Hermitian。这些系统分别称为Quasifree和Quadratic。我们发现，具有有限范围相互作用的一维系统的稳态必须呈指数型衰减的Green功能。对于没有二次lindblad运算符的准式情况，我们表明具有有限范围相互作用的费米子系统对于任何数量的空间维度都是非临界的，并且在相关长度上提供了界限。准骨系统在$ d> 1 $尺寸中至关重要。最后，我们解决了二次系统中的相变问题，发现在单粒子基础和粒子孔变换下没有超出不变性的对称约束，所有gapped liouvillians都属于同一阶段。
We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasifree and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions. For the quasifree case without quadratic Lindblad operators, we show that fermionic systems with finite-range interactions are noncritical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasifree bosonic systems can be critical in $D>1$ dimensions. Last, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase.
