Center for Molecular Modeling - P. Claeys

Variational method for integrability-breaking Richardson-Gaudin models

claeys — Mon, 30 Oct 2017 17:20:00 +0000

P. Claeys, J.-S. Caux, D. Van Neck, S. De Baerdemacker

Physical Review B

96, 155149

2017

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

DOI

http://dx.doi.org/10.1103/PhysRevB.96.155149

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PhysRevB.96.155149.pdf

Inner products in integrable Richardson-Gaudin models

claeys — Mon, 30 Oct 2017 17:16:15 +0000

P. Claeys, D. Van Neck, S. De Baerdemacker

Scipost Physics

3, 028

2017

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

DOI

http://dx.doi.org/10.21468/SciPostPhys.3.4.028

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SciPostPhys.3.4.028.pdf

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

wim — Mon, 01 Aug 2016 10:06:08 +0000

P. Claeys, S. De Baerdemacker, D. Van Neck

Physical Review B

93 (22), 220503

2016

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

DOI

http://dx.doi.org/10.1103/PhysRevB.93.220503

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16-PhysRevB-93-220503-Claeys.pdf

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

claeys — Thu, 09 Jun 2016 15:49:10 +0000

P. Claeys, S. De Baerdemacker, D. Van Neck

Physical Review B

93 (22) 220503(R)

2016

Abstract

DOI

http://dx.doi.org/10.1103/PhysRevB.93.220503

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PhysRevB.93.220503.pdf

Maximum probability domains for Hubbard models

claeys — Tue, 01 Mar 2016 09:55:04 +0000

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

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

DOI

http://dx.doi.org/10.1080/00268976.2016.1153742

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MolPhys.00268976.2016.1153742.pdf

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

wim — Mon, 07 Dec 2015 10:18:18 +0000

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck

Journal of Physics A: Mathematical and Theoretical

48 (42), 425201

2015

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.

This paper has been selected as editor's pick

DOI

http://dx.doi.org/10.1088/1751-8113/48/42/425201

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15-JPhysA-48-425201-Claeys.pdf

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

wim — Fri, 12 Jun 2015 08:56:57 +0000

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck

Journal of Physics Conference Series

597, UNSP 012025

2015

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

DOI

http://dx.doi.org/10.1088/1742-6596/597/1/012025

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15_JPhysConf.597.012025_Claeys.pdf

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

wim — Tue, 07 Apr 2015 07:01:00 +0000

P. Claeys, S. De Baerdemacker, M. Van Raemdonck, D. Van Neck

Physical Review B

91 (15), 155102

2015

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

DOI

http://dx.doi.org/10.1103/PhysRevB.91.155102

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15_PhysRevB_91(15)155102_Claeys.pdf

Richardson-Gaudin models and broken integrability

wim — Tue, 22 May 2018 07:25:00 +0000

P. Claeys

Fri, 18/05/2018

Museum voor de geschiedenis van de wetenschappen, Krijgslaan 281, 9000 Gent

https://biblio.ugent.be/publication/8564030

Supervisors

Prof. Dr. Dimitri Van Neck, Dr. Stijn De Baerdemacker

Integrable quantum many-body systems

wim — Fri, 02 Mar 2018 09:32:22 +0000