Exactly solvable pairing model for superconductors with a p+ip-wave symmetry

Abstract

We present the exact Bethe ansatz solution for the two-dimensional BCS pairing Hamiltonian with p_x + i p_y symmetry. Using both mean-field theory and the exact solution we obtain the ground-state phase diagram parameterized by the filling fraction and the coupling constant. It consists of three phases denoted weak coupling BCS, weak pairing, and strong pairing. The first two phases are separated by a topologically protected line where the exact ground state is given by the Moore-Read pfaffian state. In the thermodynamic limit the ground-state energy is discontinuous on this line. The other two phases are separated by the critical line, also topologically protected, previously found by Read and Green. We establish a duality relation between the weak and strong pairing phases, whereby ground states of the weak phase are "dressed" versions of the ground states of the strong phase by zero energy (Moore-Read) pairs and characterized by a topological order parameter.

4 pages, 2 figures. Discussion on winding numbers added. Accepted in Phys Rev B

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Quantum phase transitions from topology in momentum space
• Exact mesoscopic correlation functions of the pairing model
• Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs

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