论文标题
对称分辨的Rényi保真度和量子相变
Symmetry-resolved Rényi fidelities and quantum phase transitions
论文作者
论文摘要
我们介绍了一个量子rényi保真度的家族，并讨论他们的对称性解决方案。我们表达了对称性分辨的保真度，就像带电的忠诚度的傅立叶变换，为此我们得出了高斯州的精确公式。这些结果还产生了高斯州的总忠诚度的公式，我们希望这将在本文的范围之内使用。我们研究了XX自旋链中的总和对称性分辨的保真度，并关注（i）热状态之间的保真度，以及（ii）在零温度下降低密度矩阵之间的保真度。热和减少的保真度都可以检测XX自旋链的量子相变。此外，我们认为对称性分辨的保真度对状态的内部结构敏感。特别是，他们可以通过在临界点的电荷扇区重组来检测相变。这是对称性分辨的忠诚度的主要特征，我们期望成为一般。我们还强调，减少的保真度可以在热力学极限下检测量子相变。
We introduce a family of quantum Rényi fidelities and discuss their symmetry resolution. We express the symmetry-resolved fidelities as Fourier transforms of charged fidelities, for which we derive exact formulas for Gaussian states. These results also yield a formula for the total fidelities of Gaussian states, which we expect to have applications beyond the scope of this paper. We investigate the total and symmetry-resolved fidelities in the XX spin chain, and focus on (i) fidelities between thermal states, and (ii) fidelities between reduced density matrices at zero temperature. Both thermal and reduced fidelities can detect the quantum phase transition of the XX spin chain. Moreover, we argue that symmetry-resolved fidelities are sensitive to the inner structure of the states. In particular, they can detect the phase transition through the reorganisation of the charge sectors at the critical point. This a main feature of symmetry-resolved fidelities which we expect to be general. We also highlight that reduced fidelities can detect quantum phase transitions in the thermodynamic limit.
