自由费米子动力学量子相变中的对数奇异性
Logarithmic singularity in a dynamical quantum phase transition for free fermions
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- University of Birmingham（伯明翰大学）
- Santa Fe Institute（圣塔菲研究所）
- Université Paris-Saclay（巴黎萨克雷大学）
- Université de Toulouse（图卢兹大学）
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中文总结 AI 辅助
本研究通过Loschmidt回声研究自由费米子系统的动力学量子相变，发现动力学自由能出现对数奇异性，并将其解释为瞬子构型的拓扑变化，且后选择可驱动两次连续相变。
中文摘要 AI 辅助
我们研究了从双畴壁初始态释放的N个无相互作用无自旋格点费米子系统中的Loschmidt回声。在大N极限下，返回概率由大偏差率函数表征，该函数称为动力学自由能。Loschmidt回声由复瞬子构型主导，动力学自由能在动力学量子相变处发展出对数奇异性。我们获得了短时间和长时间区域的解析结果，并通过数值计算加以验证。我们表明，该相变可以理解为占主导地位的瞬子构型的拓扑变化，类似于随机矩阵理论中割线的出现。我们进一步表明，后选择可以驱动系统经历两次连续的动力学量子相变（DQPT），这些相变与复时间中占主导地位的瞬子构型的连续拓扑变化相关。
英文摘要
We study the Loschmidt echo in a system of N non-interacting spinless lattice fermions released from a double-domain-wall initial state. In the large-N limit, the return probability is characterized by a large-deviation rate function known as the dynamical free energy. The Loschmidt echo is dominated by a complex instanton configuration, and the dynamical free energy develops a logarithmic singularity at the dynamical quantum phase transition. We obtain analytical results in the short-time and long-time regimes and support them with numerical computations. We show that the transition can be understood as a topological change of the dominant instanton configuration, analogous to the emergence of a cut in random matrix theory. We further show that post-selection can drive the system through two successive DQPTs, associated with successive topological changes of the dominant instanton configuration in complex time.
