A Class of Exactly Solvable Pairing Models

We present three classes of exactly solvable models for fermion and boson systems, based on the pairing interaction. These models are solvable in any dimension. As an example we show the first results for fermion interacting with repulsive pairing forces in a two dimensional square lattice. Inspite of the repulsive pairing force the exact results show attractive pair correlations.Comment: 5 pages, 1 figur

Structure of the number projected BCS wave function

We study the structure of the number projected BCS (PBCS) wave function in the particle-hole basis, displaying its similarities with coupled clusters theory (CCT). The analysis of PBCS together with several modifications suggested by the CCT wave function is carried out for the exactly solvable Richardson model involving a pure pairing hamiltonian acting in a space of equally-spaced doubly-degenerate levels. We point out the limitations of PBCS to describe the non-superconducting regime and suggest possible avenues for improvement.Comment: 6 pages, 4 figures. To be published in Phys. Rev.

Improvement to the Projected BCS Approximation

6 págs.; 1 fig.; XXXVIII Symposium on Nuclear Physics (Cocoyoc 2015); Open Access funded by Creative Commons Atribution Licence 3.0We consider the structure of the number projected BCS wave function in the particle-hole basis, and use it to study several approximate treatments of pairing. The analysis is carried out for the exactly solvable Richardson model involving a pure pairing hamiltonian acting in a space of equally spaced doubly degenerate levels at half filling.The work was also supported in part by the Spanish MINECO under Grant No. FIS2012-34479, and in part by the US National Science Foundation under grant # 0553127.Peer Reviewe

Pairing in 4-component fermion systems: the bulk limit of SU(4)-symmetric Hamiltonians

Fermion systems with more than two components can exhibit pairing condensates of much more complex structure than the well-known single BCS condensate of spin-up and spin-down fermions. In the framework of the exactly solvable SO(8) Richardson-Gaudin model with SU(4)-symmetric Hamiltonians, we show that the BCS approximation remains valid in the thermodynamic limit of large systems for describing the ground state energy and the canonical and quasiparticle excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of collective excitations, but these do not affect the bulk energy and quasiparticle gaps.Comment: 13 pages; 2 figures; 1 tabl

Many-body characterization of particle-conserving topological superfluids

Theoretical Physic

A generalized Hill-Wheeler ansatz

The Hill-Wheeler ansatz for the total wave function, within the Generator Coordinate Method framework, is generalized by recourse to the theory of distributions. The ensuing approach allows one to obtain a basis that spans the collective subspace, without having to deal explicitly with the eigenvectors and eigenvalues of the overlap kernel. Applications to an exactly soluble model and anharmonic vibrations illustrate the present treatment.Facultad de Ciencias Exacta

Excited-state quantum phase transitions in the two-spin elliptic Gaudin model

10 págs.; 7 figs.We study the integrability of the two-spin elliptic Gaudin model for arbitrary values of the Hamiltonian parameters. The limit of a very large spin coupled to a small one is well described by a semiclassical approximation with just one degree of freedom. Its spectrum is divided into bands that do not overlap if certain conditions are fulfilled. In spite of the fact that there are no quantum phase transitions in each of the band heads, the bands show excited-state quantum phase transitions separating a region in which the parity symmetry is broken from another region in which time-reversal symmetry is broken. We derive analytical expressions for the critical energies in the semiclassical approximation, and confirm the results by means of exact diagonalizations for large systems. ©2016 American Physical SocietyWe acknowledge support from the Spanish Ministry of Economy and Competitiveness through Grants No. FIS2012- 34479, No. FIS2012-35536, and from MINECO (Spain) and FEDER (Spain) Grant No. FIS2015-63770-P.Peer Reviewe

Solving the Richardson equations close to the critical points

12 pages, 3 tables, 2 figures.--PACS nrs.: 02.30.Ik, 71.10.Li, 74.20.Fg.--Arxiv pre-print available at: http://arxiv.org/abs/math-ph/0609022We study the Richardson equations close to the critical values of the pairing strength gc, where the occurrence of divergences precludes numerical solutions. We derive a set of equations for determining the critical g values and the noncollapsing pair energies. Studying the behaviour of the solutions close to the critical points, we develop a procedure to solve numerically the Richardson equations for arbitrary coupling strength.This work was supported by Spanish DGI under grant BFM2003-05316-C02-02.Peer reviewe

Many-Body Characterization of Particle-Conserving Topological Superfluids

5 págs.; 2 figs.; PACS numbers: 74.20.-z, 03.65.Vf, 74.45.+c, 74.90.+nWhat distinguishes trivial superfluids from topological superfluids in interacting many-body systems where the number of particles is conserved? Building on a class of integrable pairing Hamiltonians, we present a number-conserving, interacting variation of the Kitaev model, the Richardson-Gaudin-Kitaev chain, that remains exactly solvable for periodic and antiperiodic boundary conditions. Our model allows us to identify fermion parity switches that distinctively characterize topological superconductivity (fermion superfluidity) in generic interacting many-body systems. Although the Majorana zero modes in this model have only a power-law confinement, we may still define many-body Majorana operators by tuning the flux to a fermion parity switch. We derive a closed-form expression for an interacting topological invariant and show that the transition away from the topological phase is of third order © 2014 American Physical SocietyJ. D. and C. E. are supported by Grant No. FIS2012- 34479 of the Spanish Ministry of Economy and Competitiveness.Peer Reviewe