具有动量相关相互作用的一维多体系统的精确解
Exact solution of a 1D many-body system with momentum dependent interactions
摘要：
我们讨论了一个一维多体模型的可区分的粒子与本地，动量依赖的两体相互作用。我们表明，该模型的费米子的限制对应于非相对论性的大规模Thirring模型的限制。这个费米子模型可以通过映射到具有反耦合常数的一维玻色子气体来精确求解。我们提供的证据表明，这种映射是非相对论性的限制之间的对偶性的大规模Thirring模型和量子sine-Gordon模型。我们还调查的问题，如果这个模型的推广，可区分的粒子是完全可解的坐标贝特anasterian，并发现，这是不是这样的。
英文摘要：
We discuss a 1D many-body model of distinguishable particles with local, momentum dependent two-body interactions. We show that the restriction of this model to fermions corresponds to the non-relativistic limit of the massive Thirring model. This fermion model can be solved exactly by a mapping to the 1D boson gas with inverse coupling constant. We provide evidence that this mapping is the non-relativistic limit of the duality between the massive Thirring model and the quantum sine-Gordon model. We also investigate the question if the generalization of this model to distinguishable particles is exactly solvable by the coordinate Bethe ansatz and find that this is not the case.
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