标题： 能量输运在$\mathbb{Z}_3$手性钟模型中的温度依赖性 显示英文标题

标题： Temperature dependence of energy transport in the $\mathbb{Z}_3$ chiral clock model

摘要： 我们采用矩阵乘积态模拟来研究一维$\mathbb{Z}_3$手征钟模型非可积区域内的能量输运。为了在整个系统中诱导非平衡稳态，我们考虑边界驱动的开放系统动力学，该动力学具有可调节温度和系统足迹的跳跃算符。给定一个稳态，我们通过最小化真实局部状态与均匀热系综局部状态之间的迹距离来诊断有效局部温度。通过尺度分析，我们在高于其无能隙和有能隙低温相的相对高温下提取了模型的输运系数。在我们考虑的中等至高温区域，无论低温物理如何，都观察到扩散输运。我们计算了能量扩散常数随模型参数的温度依赖性，包括在低温度下模型处于量子临界状态的区域。值得注意的是，即使在无能隙区域，基于幂级数展开的分析表明，可以在相对受限的设置中访问中间温度输运。尽管我们目前还无法达到可以观察到量子临界标度的温度，但我们的方法能够在广泛的温度和参数范围内访问模型的输运特性。最后，我们讨论了我们方法的局限性以及可能的扩展，例如，扩展到更低的温度。 显示英文摘要

摘要： We employ matrix product state simulations to study energy transport within the non-integrable regime of the one-dimensional $\mathbb{Z}_3$ chiral clock model. To induce a non-equilibrium steady state throughout the system, we consider open system dynamics with boundary driving featuring jump operators with adjustable temperature and footprint in the system. Given a steady state, we diagnose the effective local temperature by minimizing the trace distance between the true local state and the local state of a uniform thermal ensemble. Via a scaling analysis, we extract the transport coefficients of the model at relatively high temperatures above both its gapless and gapped low-temperature phases. In the medium-to-high temperature regime we consider, diffusive transport is observed regardless of the low-temperature physics. We calculate the temperature dependence of the energy diffusion constant as a function of model parameters, including in the regime where the model is quantum critical at the low temperature. Notably, even within the gapless regime, an analysis based on power series expansion implies that intermediate-temperature transport can be accessed within a relatively confined setup. Although we are not yet able to reach temperatures where quantum critical scaling would be observed, our approach is able to access the transport properties of the model over a broad range of temperatures and parameters. We conclude by discussing the limitations of our method and potential extensions that could expand its scope, for example, to even lower temperatures.