论文标题
边界散落的横向场iSing模型的精确解：Liouvillian光谱和动力学双重性的结构
Exact solution of the boundary-dissipated transverse field Ising model: Structure of Liouvillian spectrum and dynamical duality
论文作者
论文摘要
我们研究了由Lindblad Master方程描述的边界划分的横向场ISING模型，并在整个参数空间中精确求解了其Liouvillian频谱。通过将liouvillian映射到具有奇偶校验约束下具有虚界势能的Su-Schrieffer-Heeger模型，我们可以分析地求解速度频谱，从而严格构建了具有奇偶校验约束条件的Liouvillian频谱。我们的结果表明，liouvillian频谱显示了四个不同的结构，这些结构的特征是不同的片段。通过分析速度光谱的性能，我们可以通过分析来确定不同光谱结构之间的相边界，并证明在弱且强大的耗散区域中实现二元性关系的liouvillian间隙。此外，我们揭示了动态双重性的存在，即，只要二元关系成立，长期的放松动力学就在弱和强耗散区域表现出几乎相同的动力学行为。
We study the boundary-dissipated transverse field Ising model described by a Lindblad Master equation and exactly solve its Liouvillian spectrum in the whole parameter space. By mapping the Liouvillian into a Su-Schrieffer-Heeger model with imaginary boundary potentials under a parity constraint, we solve the rapidity spectrum analytically and thus construct the Liouvillian spectrum strictly with a parity constraint condition. Our results demonstrate that the Liouvillian spectrum displays four different structures, which are characterized by different numbers of segments. By analyzing the properties of rapidity spectrum, we can determine the phase boundaries between different spectrum structures analytically and prove the Liouvillian gap fulfilling a duality relation in the weak and strong dissipation region. Furthermore, we unveil the existence of a dynamical duality, i.e., the long-time relaxation dynamics exhibits almost the same dynamical behavior in the weak and strong dissipation region as long as the duality relation holds true.
