P. Claeys

Variational method for integrability-breaking Richardson-Gaudin models

P. Claeys, J.-S. Caux, D. Van Neck, S. De Baerdemacker
Physical Review B
96, 155149
2017
A1

Abstract 

We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of integrability allows for an efficient evaluation and minimization of the energy functional. The method is shown to return exact results for integrable models and improve substantially on perturbation theory for models close to integrability. For large integrability-breaking interactions, it is shown how (avoided) level crossings necessitate the use of excited states of integrable Hamiltonians in order to accurately describe the ground states of general nonintegrable models.

Green Open Access

Inner products in integrable Richardson-Gaudin models

P. Claeys, D. Van Neck, S. De Baerdemacker
Scipost Physics
3, 028
2017
A1

Abstract 

We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the states is on-shell arises naturally by demanding that a state has a dual representation. By implicitly combining these different representations, inner products can be recast as domain wall boundary partition functions. The structure of all involved matrices in terms of Cauchy matrices is made explicit and used to show how one of the classes returns the Slavnov determinant formula.
Furthermore, this framework provides a further connection between two different approaches for integrable models, one in which everything is expressed in terms of rapidities satisfying Bethe equations, and one in which everything is expressed in terms of the eigenvalues of conserved charges, satisfying quadratic equations.

Open Access version available at UGent repository
Gold Open Access

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

P. Claeys, S. De Baerdemacker, D. Van Neck
Physical Review B
93 (22), 220503
2016
A1

Abstract 

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.

Open Access version available at UGent repository

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

P. Claeys, S. De Baerdemacker, D. Van Neck
Physical Review B
93 (22) 220503(R)
2016
A1

Abstract 

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.

Maximum probability domains for Hubbard models

G. Acke, S. De Baerdemacker, P. Claeys, M. Van Raemdonck, W. Poelmans, D. Van Neck, P. Bultinck
Molecular Physics
114 (7-8), 1392-1405
2016
A1

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.

Open Access version available at UGent repository

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

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck
Journal of Physics A: Mathematical and Theoretical
48 (42), 425201
2015
A1

Abstract 

Starting from integrable su(2) (quasi-)spin Richardson–Gaudin (RG) 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 (p + ip)-wave pairing Hamiltonian. The pseudo-deformation of the underlying su(2) algebra is here introduced as a way to obtain these models in the contraction limit of different RG models. This allows for the construction of the full set of conserved charges, the Bethe ansatz state, and the resulting RG 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 RG XXZ models.

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

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck
Journal of Physics Conference Series
597, UNSP 012025
2015
P1

Abstract 

The Dicke model is derived in the contraction limit of a pseudo-deformation of the quasispin algebra in the su(2)-based Richardson-Gaudin models. Likewise, the integrability of the Dicke model is established by constructing the full set of conserved charges, the form of the Bethe Ansatz state, and the associated Richardson-Gaudin equations. Thanks to the formulation in terms of the pseudo-deformation, the connection from the su(2)-based Richardson-Gaudin model towards the Dicke model can be performed adiabatically.

Open Access version available at UGent repository

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

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck
Physical Review B
91 (15), 155102
2015
A1

Abstract 

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., Phys. Rev. B 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.

Open Access version available at UGent repository

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