Jian Shao-Kai, Liu Chunxiao, Chen Xiao, Swingle Brian, Zhang Pengfei
Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA.
Phys Rev Lett. 2021 Oct 1;127(14):140601. doi: 10.1103/PhysRevLett.127.140601.
We construct Brownian Sachdev-Ye-Kitaev (SYK) chains subjected to continuous monitoring and explore possible entanglement phase transitions therein. We analytically derive the effective action in the large-N limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. In the noninteracting case with SYK_{2} chains, the model features a continuous O(2) symmetry between two replicas and a transition corresponding to spontaneous breaking of that symmetry upon varying the measurement rate. In the symmetry broken phase at low measurement rate, the emergent replica criticality associated with the Goldstone mode leads to a log-scaling entanglement entropy that can be attributed to the free energy of vortices. In the symmetric phase at higher measurement rate, the entanglement entropy obeys area-law scaling. In the interacting case, the continuous O(2) symmetry is explicitly lowered to a discrete C_{4} symmetry, giving rise to volume-law entanglement entropy in the symmetry-broken phase due to the enhanced linear free energy cost of domain walls compared to vortices. The interacting transition is described by C_{4} symmetry breaking. We also verify the large-N critical exponents by numerically solving the Schwinger-Dyson equation.
我们构建了受连续监测的布朗型萨赫德夫 - 叶 - 基塔耶夫（SYK）链，并探索其中可能的纠缠相变。我们在大N极限下解析地推导了有效作用量，并表明纠缠相变是由扩展复本空间中的对称性破缺引起的。在具有SYK₂链的非相互作用情况下，该模型在两个复本之间具有连续的O(2)对称性，并且在改变测量速率时会出现对应于该对称性自发破缺的相变。在低测量速率下的对称破缺相中，与戈德斯通模式相关的涌现复本临界性导致对数标度的纠缠熵，这可归因于涡旋的自由能。在较高测量速率下的对称相中，纠缠熵遵循面积律标度。在相互作用情况下，连续的O(2)对称性明确降低为离散的C₄对称性，由于与涡旋相比畴壁的线性自由能成本增加，在对称破缺相中产生体积律纠缠熵。相互作用相变由C₄对称性破缺描述。我们还通过数值求解施温格 - 戴森方程验证了大N临界指数。
