来自子格依赖相互作用的例外Luttinger液体
Exceptional Luttinger Liquids from sublattice dependent interaction
AI总结：
本研究在具有子格依赖相互作用的一维晶格模型的Luttinger液体理论中发现例外点，揭示厄米体系中单粒子格林函数的非厄米拓扑性质，并通过数值与微扰方法验证了相关结论。
摘要：
我们展示了例外点（Exceptional Points, EPs）如何自然出现在Luttinger液体（Luttinger Liquid, LL）理论中，该理论描述具有子格依赖电子-电子相互作用的微观晶格模型的低能激发。在玻色化处理后，这种子格依赖性直接转化为一种非标准的sine-Gordon型项，正是该项导致了单粒子格林函数（Green Function, GF）的非厄米矩阵结构。由于激发寿命的结构与底层的自由布洛赫哈密顿量不对易，尽管我们的模型哈密顿量是厄米的，单粒子GF仍呈现出非厄米拓扑性质。例外点的形成需要同时满足有限温度和非平庸Luttinger参数$K\ eq 1$两个条件，且它们在一维空间中的拓扑稳定性由模型的手征对称性保证。在存在上述sine-Gordon项的情况下，我们采用一阶微扰论（Perturbation Theory, PT）计算单粒子GF。通过与守恒二阶玻恩近似下的数值模拟对比，以及在弱相互作用和高温条件下与费米子普通微扰论的对比，所有在LL理论框架内得到的定性结论都得到了证实。在特定参数区域内，通过在有效玻色化模型中选择合适的参数，可以达到定量一致。
英文摘要：
We demonstrate how Exceptional Points (EPs) naturally occur in the Luttinger Liquid (LL) theory describing the low-energy excitations of a microscopic lattice model with sublattice dependent electron-electron interaction. Upon bosonization, this sublattice dependence directly translates to a non-standard sine-Gordon-type term responsible for the non-Hermitian matrix structure of the single-particle Green Function (GF). As the structure in the lifetime of excitations does not commute with the underlying free Bloch Hamiltonian, non-Hermitian topological properties of the single-particle GF emerge -- despite our Hermitian model Hamiltonian. Both finite temperature and a non-trivial Luttinger parameter $K\neq 1$ are required for the formation of EPs, and their topological stability in one spatial dimension is guaranteed by the chiral symmetry of our model. In the presence of the aforementioned sine-Gordon-term, we resort to leading order Perturbation Theory (PT) to compute the single-particle GF. All qualitative findings derived within LL theory are corroborated by comparison to both numerical simulations within the conserving second Born approximation, and, for weak interactions and high temperatures, by fermionic plain PT. In certain parameter regimes, quantitative agreement can be reached by a suitable parameter choice in the effective bosonized model.
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