标题： 自旋-1/2 伊辛链的动力学结构因子与长程相互作用 显示英文标题

标题： Dynamic structure factor of a spin-1/2 Heisenberg chain with long-range interactions

摘要： 我们研究了自旋-1/2 链的动态结构因子 $S(k,\omega)$，该链具有长程、以幂律衰减的无 frustrations（符号交替）的 Heisenberg 相互作用 $J_r \sim (-1)^{r-1} r^{-\alpha}$。我们通过量子蒙特卡洛计算得到的虚时间相关函数的随机解析延拓（SAC）方法进行研究。 我们在长程反铁磁（AFM，对于 $\alpha \lesssim 2.23$）和准长程有序（QLRO，对于 $\alpha \gtrsim 2.23$）基态相中进行这项研究，采用不同的 SAC 参数化方法 $S(k,\omega)$来解析特征分数准粒子的尖锐边缘以及预期的传统准粒子的尖峰。 为了确定最准确的参数化，我们应用了一种新开发的交叉验证方法作为“模型选择”工具。 我们确认，在准长程有序相中，谱函数包含幂律发散边缘，在反铁磁相中包含非常尖锐（可能是 $\delta$- 函数）的磁振子峰值。 从我们的 SAC 结果中，我们提取了不同参数区域中的色散关系，并在反铁磁相中提取了磁振子极点的权重。 当模型退化为传统的最近邻相互作用的 Heisenberg 链时，我们的 $S(k,\omega)$结果与已知的 Bethe 方程结果吻合得很好。 在AFM相中，已知低能色散关系是非线性的，$\omega_k \sim k^z$，我们提取了相应的动力学指数$z(\alpha)$，它通常略高于线性自旋波理论得到的形式。 我们还发现，在自旋波峰值之上存在显著的连续谱。 本研究为SAC/QMC研究从常规准粒子到分数化准粒子的系统转变提供了基准。 显示英文摘要

摘要： We study the dynamic structure factor $S(k,\omega)$ of the spin-1/2 chain with long-range, power-law decaying unfrustrated (sign alternating) Heisenberg interactions $J_r \sim (-1)^{r-1} r^{-\alpha}$ by means of stochastic analytic continuation (SAC) of imaginary-time correlations computed by quantum Monte Carlo calculations. We do so in both the long-range antiferromagnetic (AFM, for $\alpha \lesssim 2.23$) and quasi-long-range-ordered (QLRO, for $\alpha \gtrsim 2.23$) ground-state phases, employing different SAC parametrizations of $S(k,\omega)$ to resolve sharp edges characteristic of fractional quasi-particles and sharp peaks expected with conventional quasi-particles. In order to identify the most statistically accurate parametrization, we apply a newly developed cross-validation method as a ``model selection'' tool. We confirm that the spectral function contains a power-law divergent edge in the QLRO phase and a very sharp (likely $\delta$-function) magnon peak in the AFM phase. From our SAC results, we extract the dispersion relation in the different regimes of the model, and in the AFM phase we extract the weight of the magnon pole. In the limit where the model reduces to the conventional Heisenberg chain with nearest-neighbor interactions, our $S(k,\omega)$ agrees well with known Bethe ansatz results. In the AFM phase the low-energy dispersion relation is known to be nonlinear, $\omega_k \sim k^z$, and we extract the corresponding dynamic exponent $z(\alpha)$, which in general is somewhat above the form obtained in linear spin-wave theory. We also find a significant continuum above the magnon peak. This study serves as a benchmark for SAC/QMC studies of systems with a transition from conventional to fractionalized quasi-particles.