边界耗散横场Ising模型的精确解：Liouvillian谱结构与动力学对偶性
Exact solution of the boundary-dissipated transverse field Ising model: Structure of Liouvillian spectrum and dynamical duality
AI总结：
该研究精确求解边界耗散横场Ising模型的Liouvillian谱，揭示其四种结构与相界，证明弱强耗散区的能隙对偶性及长时间弛豫的动力学对偶性。
摘要：
我们研究由Lindblad主方程描述的边界耗散横场Ising模型，并在全参数空间内精确求解其Liouvillian谱。通过将Liouvillian映射为宇称约束下带虚边界势的Su-Schrieffer-Heeger模型，我们解析求解了快度谱，进而严格构造出满足宇称约束条件的Liouvillian谱。结果表明，Liouvillian谱呈现四种不同结构，可通过不同的分段数量表征。通过分析快度谱的性质，我们能够解析确定不同谱结构之间的相界，并证明Liouvillian能隙在弱耗散区和强耗散区满足对偶关系。此外，我们揭示了动力学对偶性的存在：只要对偶关系成立，弱耗散区和强耗散区的长时间弛豫动力学表现出几乎相同的动力学行为。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
