论文标题
来自量子对称性的爆米花drude重量
Popcorn Drude weights from quantum symmetry
论文作者
论文摘要
可集成的模型提供了非共性现象的象征示例。他们最杰出的特性之一是有限的灌木重量发出的不同零频率电导率。奇异电导率归功于长寿命的准粒子激发，这些激发在没有任何衍射的情况下通过系统传播。著名的Quantum Heisenberg连锁店的案例是最有研究的多体范式之一，事实证明这是特别神秘的。大约十年前，发现该模型临界阶段的自旋笔重假设了一个非凡的，无处可连续的，依赖于“爆米花函数”形状的各向异性参数。随后在基本变形的量子对称代数的水平上解决了这一前所未有的发现，这有助于解释在相互作用各向异性的相应值下解释准粒子谱的不稳定性。这项工作致力于令人着迷的不连续权重的现象，目的是通过重新审视和调和以前的研究的各种观点来对这个话题进行更广泛的看法。 Moreover, it is argued that such an anomalous non-ergodic feature is not exclusive to the integrable spin chain but can be instead expected in a number of other integrable systems that arise from realizations of the quantum group $\mathcal{U}_{q}(\mathfrak{sl}(2))$, specialized to unimodular values of the quantum deformation parameter $q$.我们的讨论是在较高自旋的无间隙各向异性量子链和正弦量子量子场理论的背景下进行的。
Integrable models provide emblematic examples of non-ergodic phenomena. One of their most distinguished properties are divergent zero-frequency conductivities signalled by finite Drude weights. Singular conductivities owe to long-lived quasiparticle excitations that propagate ballistically through the system without any diffraction. The case of the celebrated quantum Heisenberg chain, one of the best-studied many-body paradigms, turns out to be particularly mysterious. About a decade ago, it was found that the spin Drude weight in the critical phase of the model assumes an extraordinary, nowhere continuous, dependence on the anisotropy parameter in the shape of a `popcorn function'. This unprecedented discovery has been afterwards resolved at the level of the underlying deformed quantum symmetry algebra which helps explaining the erratic nature of the quasiparticle spectrum at commensurate values of interaction anisotropy. This work is devoted to the captivating phenomenon of discontinuous Drude weights, with the aim to give a broader perspective on the topic by revisiting and reconciling various perspectives from the previous studies. Moreover, it is argued that such an anomalous non-ergodic feature is not exclusive to the integrable spin chain but can be instead expected in a number of other integrable systems that arise from realizations of the quantum group $\mathcal{U}_{q}(\mathfrak{sl}(2))$, specialized to unimodular values of the quantum deformation parameter $q$. Our discussion is framed in the context of gapless anisotropic quantum chains of higher spin and the sine-Gordon quantum field theory in two space-time dimensions.
