推广的d+ id-波配对哈密顿量的可积性
Integrability of an extended d+id-wave pairing Hamiltonian
摘要：
我们引入了一个可积的哈密顿量，它是一个扩展的d+ id波配对模型。可积性推导出的Richardson-Gaudin（s波）配对模型的对偶关系，并与此相关联的存在一个精确的Bethe anomaly的解决方案。我们使用连续极限方法研究了这个系统，并求解了相应的奇异积分方程，得到了Bethe渐近解。我们还进行了平均场分析，并表明，从这两种方法的结果相吻合的连续极限的基态。我们确定的可积系统的激发光谱是无缝的情况下，并讨论连接到不可积模型与d+ id波配对相互作用，通过平均场分析。
英文摘要：
We introduce an integrable Hamiltonian which is an extended d+id-wave pairing model. The integrability is deduced from a duality relation with the Richardson-Gaudin (s-wave) pairing model, and associated to this there exists an exact Bethe ansatz solution. We study this system using the continuum limit approach and solve the corresponding singular integral equation obtained from the Bethe ansatz solution. We also conduct a mean-field analysis and show that results from these two approaches coincide for the ground state in the continuum limit. We identify instances of the integrable system where the excitation spectrum is gapless, and discuss connections to non-integrable models with d+id-wave pairing interactions through the mean-field analysis.
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