可积量子晶格模型中扩散输运和弹道输运的共存
Coexistence of diffusive and ballistic transport in integrable quantum lattice models
摘要：
研究了两种一维可积量子晶格模型：各向异性XXZ自旋链和Hubbard链中的高温动态电导率$σ(ω)$。重点是两种模型的金属制度，其中除了弹道组件，导电性的常规部分可能会揭示一个类似扩散的运输。为了解决低频动力学问题，我们改进了微正则Lanczos方法，使之能够研究XXZ自旋模型的有限尺寸系统，使之具有频率分辨率$L\leq 32$. XXZ链的结果揭示了精细结构的$σ(ω)$光谱，这源于不连续的变化的刚度，以前发现在相称的值的各向异性参数$Δ$。尽管如此，我们没有发现扩散成分的明确证据，至少没有发现$Δ$的相称值，特别是$Δ=0.5$和$Δ\to 0$。对于远离半填充的哈伯德模型也得到类似的结论，其中光谱揭示了更普遍的行为。
英文摘要：
We investigate the high-temperature dynamical conductivity $σ(ω)$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where besides the ballistic component, the regular part of conductivity might reveal a diffusive-like transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to $L\leq 32$ sites for XXZ spin model with the frequency resolution $δω\sim 10^{-3} J$. Results for the XXZ chain reveal a fine structure of $σ(ω)$ spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter $Δ$. Still, we do not find a clear evidence for a diffusive component, at least not for commensurate values of $Δ$, particularly for $Δ=0.5$, as well as for $Δ\to 0$. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.
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