Entanglement transitions with free fermions
Entanglement transitions with free fermions
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DOI：
10.1103/physrevb.107.064303
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发表时间：
2022-10
影响因子：
3.7
通讯作者：
J. Merritt;L. Fidkowski
中科院分区：
文献类型：
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作者：
J. Merritt;L. Fidkowski
我们使用马约拉纳算子来研究随机自由费米子酉演化和一维投影测量下的纠缠动力学。对于酉演化的某些选择，即那些交换相邻马约拉纳算子的选择，以及相邻马约拉纳双线性的测量，可以将演化映射到具有交叉的完全填充环（CPLC）的统计模型并研究相应的相图。我们使用费米子高斯态语言将该模型推广到作用于邻近马约拉纳算子的一般自由费米子酉演化，并数值计算其相图。我们发现戈德斯通相和面积定律相在这个新相图中仍然存在，但相界发生了变化。新相边界的一个重要的定性方面是，即使对于通勤测量的情况，戈德斯通相也能持续到有限的非零测量率。这与 CPLC 形成鲜明对比，在 CPLC 中，非通勤测量对于实现 Goldstone 阶段是必要的。我们还数值计算了相变处的相关长度临界指数，我们发现该指数与 CPLC 的相近，并对 CPLC 和广义模型之间相变线的一些差异给出了基于对称性的尝试性解释。
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.