TY - JOUR UR - http://lib.ugent.be/catalog/pug01:5712846 ID - pug01:5712846 LA - eng TI - Exact solution of the p(x) + ip(y) pairing Hamiltonian by deforming the pairing algebra PY - 2014 JO - (2014) PHYSICAL REVIEW B SN - 1098-0121 PB - 2014 AU - Van Raemdonck, Mario UGent 000070167170 802001296301 AU - De Baerdemacker, Stijn WE05 001999152418 801001767982 0000-0001-7933-3227 AU - Van Neck, Dimitri WE05 801000661071 0000-0001-9687-1895 AB - 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 (He-3), 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. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 5712846 | ||
005 | 20181113145148.0 | ||
008 | 140929s2014------------------------eng-- | ||
022 | a 1098-0121 | ||
024 | a 000337301200001 2 wos | ||
024 | a 1854/LU-5712846 2 handle | ||
024 | a 10.1103/PhysRevB.89.155136 2 doi | ||
040 | a UGent | ||
245 | a Exact solution of the p(x) + ip(y) pairing Hamiltonian by deforming the pairing algebra | ||
260 | c 2014 | ||
520 | a 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 (He-3), 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. | ||
598 | a A1 | ||
700 | a Van Raemdonck, Mario u UGent 0 000070167170 0 802001296301 0 979952868892 9 06568C40-F0EE-11E1-A9DE-61C894A0A6B4 | ||
700 | a De Baerdemacker, Stijn u WE05 0 001999152418 0 801001767982 0 0000-0001-7933-3227 9 F6D1E526-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Van Neck, Dimitri u WE05 0 801000661071 0 0000-0001-9687-1895 9 F44C0836-F0ED-11E1-A9DE-61C894A0A6B4 | ||
650 | a Physics and Astronomy | ||
653 | a SYSTEMS | ||
653 | a SUPERFLUIDS | ||
653 | a MODELS | ||
773 | t PHYSICAL REVIEW B g Phys. Rev. B. 2014. 89 (15) q 89:15< | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/5712846/file/5712873 z [open] y 14_phys_rev_B_89_15_155136_Van_Raemdonck.pdf | ||
920 | a article | ||
Z30 | x WE 1 WE05 | ||
922 | a UGENT-WE |
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