Pieter W. Claeys

Eigenvalue-based method and form-factor determinant representations for integrable XXZ Richardson-Gaudin models

We propose an extension of the numerical approach for integrable Richardson-Gaudin models based on a new set of eigenvalue-based variables [A. Faribault et al., Phys. Rev. B 83, 235124 (2011); O. El Araby et al., ibid. 85, 115130 (2012)]. Starting solely from the Gaudin algebra, the approach is generalized towards the full class of XXZ Richardson-Gaudin models. This allows for a fast and robust numerical determination of the spectral properties of these models, avoiding the singularities usually arising at the so-called singular points. We also provide different determinant expressions for the normalization of the Bethe ansatz states and form factors of local spin operators, opening up possibilities for the study of larger systems, both integrable and nonintegrable. These expressions can be written in terms of the new set of variables and generalize the results previously obtained for rational Richardson-Gaudin models [A. Faribault and D. Schuricht, J. Phys. A 45, 485202 (2012)] and Dicke-Jaynes-Cummings-Gaudin models [H. Tschirhart and A. Faribault, J. Phys. A 47, 405204 (2014)]. Remarkably, these results are independent of the explicit parametrization of the Gaudin algebra, exposing a universality in the properties of Richardson-Gaudin integrable systems deeply linked to the underlying algebraic structure.

Read-Green resonances in a topological superconductor coupled to a bath

We study a topological superconductor capable of exchanging particles with an environment. This additional interaction breaks particle-number symmetry and can be modeled by means of an integrable Hamiltonian, building on the class of Richardson-Gaudin pairing models. The isolated system supports zero-energy modes at a topological phase transition, which disappear when allowing for particle exchange with an environment. However, it is shown from the exact solution that these still play an important role in system-environment particle exchanges, which can be observed through resonances in low-energy and low-momentum level occupations. These fluctuations signal topologically protected Read-Green points and cannot be observed within traditional mean-field theory.

Eigenvalue-based determinants for scalar products and form factors in Richardson-Gaudin integrable models coupled to a bosonic mode

Starting from integrable

Maximum Probability Domains for Hubbard Models

su(2)

The Dicke model as the contraction limit of a pseudo-deformed Richardson-Gaudin model

(quasi-)spin Richardson-Gaudin XXZ models we derive several properties of integrable spin models coupled to a bosonic mode. We focus on the Dicke-Jaynes-Cummings-Gaudin models and the two-channel

Something interacting and solvable in 1d

(p+ip)

Spin Polarization through Floquet Resonances in a Driven Central Spin Model

-wave pairing Hamiltonian. The pseudo-deformation of the underlying

Inner products in integrable Richardson-Gaudin models

su(2)

Out-of-equilibrium phase transitions induced by Floquet resonances in a periodically quench-driven XY spin chain.

algebra is here introduced as a way to obtain these models in the contraction limit of different Richardson-Gaudin models. This allows for the construction of the full set of conserved charges, the Bethe Ansatz state, and the resulting Richardson-Gaudin equations. For these models an alternative and simpler set of quadratic equations can be found in terms of the eigenvalues of the conserved charges. Furthermore, the recently proposed eigenvalue-based determinant expressions for the overlaps and form factors of local operators are extended to these models, linking the results previously presented for the Dicke-Jaynes-Cummings-Gaudin models with the general results for Richardson-Gaudin XXZ models.

Richardson-Gaudin models and broken integrability

ABSTRACT The theory of maximum probability domains (MPDs) is formulated for the Hubbard model in terms of projection operators and generating functions for both exact eigenstates as well as Slater determinants. A fast MPD analysis procedure is proposed, which is subsequently used to analyse numerical results for the Hubbard model. It is shown that the essential physics behind the considered Hubbard models can be exposed using MPDs. Furthermore, the MPDs appear to be in line with what is expected from Valence Bond (VB) Theory-based knowledge.