Dynamical quantum phase transitions in Sachdev-Ye-Kitaev Lindbladians
Dynamical quantum phase transitions in Sachdev-Ye-Kitaev Lindbladians
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DOI：
10.1103/physrevb.108.075110
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发表时间：
2022-10
影响因子：
3.7
通讯作者：
K. Kawabata;A. Kulkarni;Jiachen Li;Tokiro Numasawa;S. Ryu
中科院分区：
文献类型：
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作者：
K. Kawabata;A. Kulkarni;Jiachen Li;Tokiro Numasawa;S. Ryu
我们研究了由Lindblad主方程描述的Sachdev-Ye-Kitaev （SYK）模型的开放量子动力学，其中SYK模型耦合到马约拉纳费米子算子中具有线性或二次跳变算子的马尔可夫库。我们特别感兴趣的是耗散形状因子的时间演化，它量化了初始和时间演化密度矩阵之间的平均重叠，作为洛施密特回波的开放量子推广。我们发现耗散形状因子表现出动态量子相变。我们解析地证明了在大量费米子味态的极限下存在不连续的动态相变，其形式类似于黑洞和虫洞相之间的双耦合SYK模型中的热相变。我们还发现在双耦合SYK模型中没有对应的连续动态相变。虽然相变在大量费米子口味的限制下是尖锐的，但它们的定性特征即使在有限数量的费米子口味中也存在，正如我们在数值上所示。
We study the open quantum dynamics of the Sachdev-Ye-Kitaev (SYK) model described by the Lindblad master equation, where the SYK model is coupled to Markovian reservoirs with jump operators that are either linear or quadratic in the Majorana fermion operators. Of particular interest for us is the time evolution of the dissipative form factor, which quantifies the average overlap between the initial and time-evolved density matrices as an open quantum generalization of the Loschmidt echo. We find that the dissipative form factor exhibits dynamical quantum phase transitions. We analytically demonstrate a discontinuous dynamical phase transition in the limit of large number of fermion flavors, which is formally akin to the thermal phase transition in the two-coupled SYK model between the black-hole and wormhole phases. We also find continuous dynamical phase transitions that do not have counterparts in the two-coupled SYK model. While the phase transitions are sharp in the limit of large number of fermion flavors, their qualitative signatures are present even for the finite number of fermion flavors, as we show numerically.