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Exact solution of the p_x + ip_y pairing Hamiltonian by deforming the pairing algebra

机译：通过变形配对代数来精确求解p_x + ip_y配对哈密顿量

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Recently, interest has increased in the hyperbolic family of integrable Richardson-Gaudin (RG) models. It was pointed out that a particular linear combination of the integrals of motion of the hyperbolic RG model leads to a Hamiltonian that describes p-wave pairing in a two-dimensional system. Such an interaction is found to be present in fermionic superfluids (~3He), ultracold atomic gases, and p-wave superconductivity. Furthermore the phase diagram is intriguing, with the presence of the Moore-Read and Read-Green lines. At the Read-Green line a rare third-order quantum phase transition occurs. The present paper makes a connection between collective bosonic states and the exact solutions of the p_x + ip_y pairing Hamiltonian. This makes it possible to investigate the effects of the Pauli principle on the energy spectrum, by gradually reintroducing the Pauli principle. It also introduces an efficient and stable numerical method to probe all the eigenstates of this class of Hamiltonians. We extend the phase diagram to repulsive interactions, an area that was not previously explored due to the lack of a proper mean-field solution in this region. We found a connection between the point in the phase diagram where the ground state connects to the bosonic state with the highest collectivity, and the Moore-Read line where all the Richardson-Gaudin (RG) variables collapse to zero. In contrast with the reduced BCS case, the overlap between the ground state and the highest collective state at the Moore-Read line is not the largest. In fact it shows a minimum when most other bosonic states show a maximum of the overlap. We found remnants of the Read-Green line for finite systems, by investigating the total spectrum. A symmetry was found between the Hamiltonian with and without single-particle part. When the interaction was repulsive we found four different classes of trajectories of the RG variables.
机译：最近，对可积Richardson-Gaudin（RG）模型的双曲族的兴趣增加了。需要指出的是，双曲线RG模型的运动积分的特定线性组合导致描述二维系统中p波对的哈密顿量。发现这种相互作用存在于铁离子超流体（〜3He），超冷原子气体和p波超导中。此外，具有摩尔读取线和绿色读取线的相位图很有趣。在“读取绿色”线处，发生了罕见的三阶量子相变。本文建立了集体玻色子状态与p_x + ip_y对哈密顿量的精确解之间的联系。通过逐步重新引入保利原理，可以研究保利原理对能谱的影响。它还引入了一种有效且稳定的数值方法来探究此类哈密顿量的所有本征态。我们将相图扩展到斥力相互作用，由于该区域缺少适当的平均场解，因此之前未进行探索。我们在相图中的基态连接到具有最高集体性的玻色状态的点与摩尔定律线之间建立了联系，在摩尔定律线中，所有Richardson-Gaudin（RG）变量都崩溃为零。与减小的BCS情况相反，摩尔阅读线的基态和最高集体状态之间的重叠不是最大的。实际上，当大多数其他玻色子状态显示出最大重叠时，它显示出最小值。通过调查总频谱，我们发现了有限系统的Read-Green线的残留物。在具有和不具有单颗粒部分的哈密顿量之间发现对称性。当相互排斥时，我们发现了RG变量的四种不同轨迹。

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