半直线上两个互补一维量子多体系统的精确解
Exact solutions of two complementary 1D quantum many-body systems on the half-line
摘要：
我们考虑两个特定的一维量子多体系统的局部相互作用与根系$C_N$。这两种模型都描述了在原点具有非平凡边界条件的半直线上运动的相同粒子，并且它们在许多方面彼此互补。我们讨论的第一个模型中的相互作用势是δ函数的贝特Anglands解决方案，我们发现，这不仅在玻色子的情况下，但即使是广义模型的粒子是可区分的，提供了一个精确的解决方案。在第二个模型中的粒子有特定的动量依赖的相互作用，我们发现，它是非平凡的和精确可解的Bethe Anonymous的情况下，粒子是费米子。后一个模型有一个自然的物理解释，作为半线上的大质量Thirring模型的非相对论极限。我们建立了玻色子δ相互作用模型和具有局域动量相关相互作用的费米模型之间的对偶关系。我们还阐述了这些模型的物理解释。在我们的讨论中，杨-巴克斯特关系和反射方程起着中心作用。
英文摘要：
We consider two particular 1D quantum many-body systems with local interactions related to the root system $C_N$. Both models describe identical particles moving on the half-line with non-trivial boundary conditions at the origin, and they are in many ways complementary to each other. We discuss the Bethe Ansatz solution for the first model where the interaction potentials are delta-functions, and we find that this provides an exact solution not only in the boson case but even for the generalized model where the particles are distinguishable. In the second model the particles have particular momentum dependent interactions, and we find that it is non-trivial and exactly solvable by Bethe Ansatz only in case the particles are fermions. This latter model has a natural physical interpretation as the non-relativistic limit of the massive Thirring model on the half-line. We establish a duality relation between the bosonic delta-interaction model and the fermionic model with local momentum dependent interactions. We also elaborate on the physical interpretation of these models. In our discussion the Yang-Baxter relations and the Reflection equation play a central role.
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