Abstract
We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.
Highlights
The model is solvable in any spatial dimension and shares some commonalities with the p + ip Richardson-Gaudin fermionic model, such as a third-order quantum phase transition
Integrable Richardson-Gaudin (RG) models [1,2] based on the su(2) fermion pair algebra have attracted a lot of attention in recent years, starting with studies of the metalto-superconductor transition in ultrasmall grains [3], where the original Richardson’s exact solution of the BCS model [4] was rediscovered, to their generalization to a broad range of phenomena in interacting quantum many-body systems [5,6]
Its repulsive version in the strong coupling limit has been shown to be related to the quantum Hall Hamiltonian projected onto the lowest Landau level subspace [19]
Summary
Integrable Richardson-Gaudin (RG) models [1,2] based on the su(2) fermion pair algebra have attracted a lot of attention in recent years, starting with studies of the metalto-superconductor transition in ultrasmall grains [3], where the original Richardson’s exact solution of the BCS model [4] was rediscovered, to their generalization to a broad range of phenomena in interacting quantum many-body systems [5,6]. The notable p + ip model of p-wave fermionic pairing [13,14,15] is an exception, having the MooreRead (MR) Pfaffian, proposed for the non-Abelian quantum Hall fluid with filling fraction 5/2 [16,17], as the ground state at a given coupling strength. Another recent finding is a number conserving version of the Kitaev wire which hosts topologically trivial and nontrivial superfluid phases [18]. It is straightforward to extend our model to higher dimensions as has been done in the fermionic case [13,14]
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