论文标题
纠缠与免费费米子的纠缠过渡
Entanglement transitions with free fermions
论文作者
论文摘要
我们使用Majorana操作员在一个维度的随机自由费用统一进化和投射测量下研究纠缠动态。对于某些统一进化的选择，即交换邻近的主要运算符的那些以及邻近的Majorana双线性的测量值，可以将演变映射到具有交叉点（CPLC）的完全包装回路的统计模型并研究相应的相图。我们使用费米子高斯状态的语言将此模型概括为一般的自由费米昂统一进化，该模型作用于邻近的Majorana操作员，并数值计算其相图。我们发现，在这个新相图中，金石和区域法阶段都持续存在，但相位边界也有所移动。新相边界的一个重要定性方面是，即使对于通勤测量的情况，戈德石期仍然持续到有限的非零测量率。这与CPLC相反，CPLC在实现戈德石相必须进行非交通测量。我们还从数值上计算过渡时的相关长度临界指数，我们发现该指数靠近CPLC的相关长度，并为CPLC和广义模型之间的相变线中的某些差异提供了基于初步对称性的解释。
We use Majorana operators to study entanglement dynamics under random free fermion unitary evolution and projective measurements in one dimension. For certain choices of unitary evolution, namely those which swap neighboring Majorana operators, and measurements of neighboring Majorana bilinears, one can map the evolution to the statistical model of completely packed loops with crossings (CPLC) and study the corresponding phase diagram. We generalize this model using the language of fermionic Gaussian states to a general free fermion unitary evolution acting on neighboring Majorana operators, and numerically compute its phase diagram. We find that both the Goldstone and area law phases persist in this new phase diagram, but with a shifted phase boundary. One important qualitative aspect of the new phase boundary is that even for the case of commuting measurements, the Goldstone phase persists up to a finite non-zero measurement rate. This is in contrast with the CPLC, in which non-commuting measurements are necessary for realizing the Goldstone phase. We also numerically compute the correlation length critical exponent at the transition, which we find to be near to that of the CPLC, and give a tentative symmetry based explanation for some differences in the phase transition line between the CPLC and generalized models.
