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arXiv · 2006.12445

Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications

Xu-Yang Hou·Qu-Cheng Gao·Hao Guo·Yan He·Tong Liu·Chih-Chun Chien
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Abstract

The Loschmidt amplitude of the purified states of mixed-state density matrices is shown to have zeros when the system undergoes a quasistatic, quench, or Uhlmann process. While the Loschmidt-amplitude zero of a quench process corresponds to a dynamical quantum phase transition (DQPT) accompanied by the diverging dynamical free energy, the Loschmidt-amplitude zero of the Uhlmann process corresponds to a topological phase transition (TQPT) accompanied by a jump of the Uhlmann phase. Although the density matrix remains intact in a quasistatic process, the Loschmidt amplitude can have zeros not associated with a phase transition. We present examples of two-level and three-level systems exhibiting finite- or infinite- temperature DQPTs and finite-temperature TQPTs associated with the Loschmidt-amplitude zeros. Moreover, the dynamical phase or geometrical phase of mixed states can be extracted from the Loschmidt amplitude. Those phases may become quantized or exhibit discontinuity at the Loschmidt-amplitude zeros. A spinor representation of the purified states of a general two-level system is presented to offer more insights into the change of purification in different processes. The quasistatic process, for example, is shown to cause a rotation of the spinor.

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Xu-Yang Hou, Qu-Cheng Gao, Hao Guo, Yan He, Tong Liu, Chih-Chun Chien. 2020-09-02. Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications. https://doi.org/10.1103/physrevb.102.104305

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