论文标题
正方形和三角形晶格莫特绝缘子在有限温度下的磁集体模式的动力学
Dynamics of magnetic collective modes in the square and triangular lattice Mott insulators at finite temperature
论文作者
论文摘要
我们研究了在正方形和三角形晶格上哈伯德模型的莫特绝缘阶段中磁矩的平衡动力学。我们根据辅助矢量场重写了哈伯德的相互作用，并使用最近开发的langevin方案来研究其动力学。大约可以从Keldysh形式主义衍生的热噪声，使我们能够研究有限温度的效果。在强耦合时，$ u \ gg t $，其中$ u $是本地排斥，而最近的邻居跳跃，我们的结果复制了最近的邻居海森伯格模型，带有Exchange $ j \ sim {\ cal o}（\ cal o}（t^2/u）$。这些包括从温度下的弱阻尼分散模式$ t \ ll j $到$ t \ sim {\ cal o}（j）$的跨界分散模式，以及$ t \ gg j $的扩散动力学。跨界温度自然与$ j $成正比。为了突出海森堡物理学的渐进偏差，因为$ u/t $降低了我们从低温旋转波速度中计算有效的交换量表$ j_ {eff}（u）$。 We discover two features in the dynamical behaviour with decreasing $U/t$: (i)~the low temperature dispersion deviates from the Heisenberg result, as expected, due to longer range and multispin interactions, and (ii)~the crossovers between weak damping, strong damping, and diffusion take place at noticeably lower values of $T/J_{eff}$.我们将其与增强的模式耦合联系起来，尤其是在较弱的$ u/t $下与热振幅波动相关联。正方形和三角形晶格的比较揭示了几何挫败感对阻尼的其他影响。
We study the equilibrium dynamics of magnetic moments in the Mott insulating phase of the Hubbard model on the square and triangular lattice. We rewrite the Hubbard interaction in terms of an auxiliary vector field and use a recently developed Langevin scheme to study its dynamics. A thermal `noise', derivable approximately from the Keldysh formalism, allows us to study the effect of finite temperature. At strong coupling, $U \gg t$, where $U$ is the local repulsion and $t$ the nearest neighbour hopping, our results reproduce the well known dynamics of the nearest neighbour Heisenberg model with exchange $J \sim {\cal O}(t^2/U)$. These include crossover from weakly damped dispersive modes at temperature $T \ll J$ to strong damping at $T \sim {\cal O}(J)$, and diffusive dynamics at $T \gg J$. The crossover temperatures are naturally proportional to $J$. To highlight the progressive deviation from Heisenberg physics as $U/t$ reduces we compute an effective exchange scale $J_{eff}(U)$ from the low temperature spin wave velocity. We discover two features in the dynamical behaviour with decreasing $U/t$: (i)~the low temperature dispersion deviates from the Heisenberg result, as expected, due to longer range and multispin interactions, and (ii)~the crossovers between weak damping, strong damping, and diffusion take place at noticeably lower values of $T/J_{eff}$. We relate this to enhanced mode coupling, in particular to thermal amplitude fluctuations, at weaker $U/t$. A comparison of the square and triangular lattice reveals the additional effect of geometric frustration on damping.
