We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models for nonlinear Luttinger liquids to the case of open boundary conditions. For integrable models, we show that boundary autocorrelations oscillate as a function of time with the same frequency as the corresponding bulk autocorrelations. This frequency can be identified as the band edge of elementary excitations. The amplitude of the oscillations decays as a power law with distinct exponents at the boundary and in the bulk, but boundary and bulk exponents are determined by the same coupling constant in the mobile impurity model. For nonintegrable models, we argue that the power-law decay of the oscillations is generic for autocorrelations in the bulk, but turns into an exponential decay at the boundary. Moreover, there is in general a nonuniversal shift of the boundary frequency in comparison with the band edge of bulk excitations. The predictions of our effective field theory are compared with numerical results obtained by time-dependent density matrix renormalization group (tDMRG) for both integrable and nonintegrable critical spin-$S$ chains with $S=1/2$, $1$ and $3/2$.
Open spin chain realization of topological defect on 1d Ising model and boundary and bulk symmetry
研究了临界开边界条件下一维量子伊辛模型中拓扑缺陷的实现.应用[M.豪鲁湾甚至，W。W. Ho，D. Gaiotto和G. Vidal，Phys. Rev. B 94，115125（2016）]，我们证明了具有多个拓扑缺陷的开链上的伊辛模型可以变换为具有边界磁场和非相互作用边界自由度的相同模型。这导致Cardy态的线性组合的出现[J. L. Cardy，Nucl.Phys.B324，581（1989）]，其可以被解释为自旋或费米子链的边缘状态。我们发现，这种边缘状态与大的边界熵下可以保护散装扰动，而它是脆弱的边界扰动。我们的配方表明存在的非平凡的边缘物理拓扑缺陷的存在下，并打开了许多有趣的问题，为未来的分析有关的边界和散装物理。
