具有长程跃迁的两腿Creutz梯子模型中的动态量子相变
Dynamic quantum phase transitions in the two-leg Creutz ladder with long-range hopping
AI总结：
本文研究具有长程跃迁的两腿Creutz模型的量子淬火，通过求解一般两带模型的精确解确定动态自由能与临界时间，发现临界时间数量随幂律指数ν和跃迁范围D变化，与SSH模型现象类似。
AI中文摘要：
本工作研究具有长程跃迁的两腿Creutz模型中的量子淬火过程，其中跃迁振幅随距离以幂律衰减，该幂律由指数ν表征，且跃迁具有有限范围D。我们首先在动量空间中得到一般两带模型的精确解，这使得我们能够计算Loschmidt振幅，进而得到该两带模型的动态自由能f(t)。我们还展示了如何通过求解非线性方程来确定Yang-Lee Fisher（YLF）零点。我们证明动量空间中的两腿Creutz模型是一般两带模型的特殊情况。利用这些结果，我们识别出动态自由能f(t)在临界时间t_c处的非解析性，发现非平凡临界时间的数量N_s同时依赖于ν和D。特别地，我们表明对于小ν和大D，临界时间变得越来越密集，在合适的参数区域会导致在越来越密集的时间集合处出现非解析性，这与Xavier和Hoyos在《Phys. Rev. B, 108, 214303 (2023)》中报道的具有长程跃迁项的Su-Schrieffer-Heeger（SSH）模型中的现象类似。
英文摘要：
In this work, we investigate quantum quenches in the two-leg Creutz model with long-range hopping, where the hopping amplitudes decay with distance as a power law characterized by an exponent $ν$ and have a finite range $D$. We first obtain the exact solution of a generic two-band model in momentum space. This allows us to compute the Loschmidt amplitude and, consequently, the dynamical free energy $f(\texttt{t})$ of the two-band model. We also show how to determine the Yang-Lee Fisher (YLF) zeros by solving a nonlinear equation. We demonstrate that the two-leg Creutz model in momentum space is a special case of the generic two-band model. Using these results, we identify the non-analyticities in the dynamical free energy $f(\texttt{t})$ at critical times $\texttt{t}_{c}$. We find that the number of nontrivial critical times $N_{s}$ depends on both $ν$ and $D$. In particular, we show that for small $ν$ and large $D$ the critical times become increasingly dense, leading, in the appropriate regime, to non-analyticities at an increasingly dense set of times---similar to what was observed by Xavier and Hoyos [Phys. Rev. B, $\textbf{108}$, 214303 (2023)] in the Su-Schrieffer-Heeger (SSH) model with long-range hopping terms.
