Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

4 Deformed Richardson-Gaudin model

P. Kulish, Alexander Stolin, H. Johannesson

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a\nfinite chain. The integrability of the Hamiltonian allows the algebraic construction of its eigenstates. In this\nwork we show that the quantum group theory provides a possibility to deform the Hamiltonian preserving\nintegrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the\nRichardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term\ninto the auxiliary L-operator which generates integrals of motion of the system. Moreover, the quantum\ninverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These\nstates have a highly complex entanglement structure which require further investigation.

Related papers

Deformed Richardson-Gaudin model

P Kulish, Alexander Stolin, L H Johannesson

The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows the algebraic construction of its eigenstates. In this work we show that the quantum group theory provides a possibility to deform the Hamiltonian preserving integrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term into the auxiliary L -operator which generates integrals of motion of the system. Moreover, the quantum inverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These states have a highly complex entanglement structure which require further investigation.

arXiv:1402.4838•Journal of Physics Conference Series•Sep 10, 2014•0 citations

Quantum deformed Richardson-Gaudin model

Henrik Johannesson, Alexander Stolin, P. P. Kulish

The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows for its eigenstates to be constructed algebraically. In this work, we show that quantum group theory provides a possibility to deform the Hamiltonian preserving integrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term into the auxiliary L-operator which generates integrals of motion of the system. Moreover, the quantum inverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These states have a highly complex entanglement structure which require further investigation.

•Jan 1, 2013•0 citations

s l 2 Gaudin model with jordanian twist

N. Cirilo António, N. Manojlović

s l 2 Gaudin model with jordanian twist is studied. This system can be obtained as the semiclassical limit of the XXX spin chain deformed by the jordanian twist. The appropriate creation operators that yield the Bethe states of the Gaudin model and consequently its spectrum are defined. Their commutation relations with the generators of the corresponding loop algebra as well as with the generating function of integrals of motion are given. The inner products and norms of Bethe states and the relation to the solutions of the Knizhnik-Zamolodchikov equations are discussed.

arXiv:nlin/0506029•Journal of Mathematical Physics•Oct 1, 2005•20 citations

Bethe ansatz for the deformed Gaudin model; pp. 326–331

P. P. Kulish, N. Manojlović, Maxim Samsonov +1 more

A deformation of the sl(2) Gaudin model by a Jordanian r-matrix depending on the spectral parameter is constructed. The energy spectrum is preserved and recurrent creation operators are proposed.

Proceedings of the Estonian Academy of Sciences•Oct 28, 2010•10 citations

Richardson-Gaudin integrable systems (and beyond) for strongly correlated quantum many-body systems

Stijn De Baerdemacker, Paul W. Ayers, Patrick Bultinck +4 more

Integrable systems take a special niche in quantum many-body systems. Due to the underlying algebraic structure, it is possible to capture all the quantum correlations exactly within a Bethe Ansatz wavefunction at a favourably scaling computational cost. Richardson [1] and Gaudin [2] have shown that the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian of superconductivity [3] is integrable and that the Bethe Ansatz state corresponds to a product wave function of generalized Cooper pairs [4]. In this formulation, the Bethe ansatz state is equivalent to a non-orthogonal geminal, which is widely used in quantum chemistry to describe electron pair correlations in atoms and molecules [5]. Inspired by Richardson-Gaudin integrable systems, it is possible to construct classes of non-orthogonal geminals, allowing for an accurate description of realistic and non-integrable strongly correlated atoms and molecules, while retaining the favorable computational scaling [6, 7]. In this contribution, I will discuss Richardson-Gaudin integrability and why it is useful for strongly correlated systems.

•Jan 1, 2013•0 citations

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

Pieter W. Claeys, Stijn De Baerdemacker, Mario Van Raemdonck +1 more

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.

arXiv:1411.5199•Journal of Physics Conference Series•Apr 13, 2015•5 citations
The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a\nfinite chain. The integrability of the Hamiltonian allows the algebraic construction of its eigenstates. In this\nwork we show that the quantum group theory provides a possibility to deform the Hamiltonian preserving\nintegrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the\nRichardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term\ninto the auxiliary L-operator which generates integrals of motion of the system. Moreover, the quantum\ninverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These\nstates have a highly complex entanglement structure which require further investigation.
The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows the algebraic construction of its eigenstates. In this work we show that the quantum group theory provides a possibility to deform the Hamiltonian preserving integrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term into the auxiliary L -operator which generates integrals of motion of the system. Moreover, the quantum inverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These states have a highly complex entanglement structure which require further investigation.
The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The integrability of the Hamiltonian allows for its eigenstates to be constructed algebraically. In this work, we show that quantum group theory provides a possibility to deform the Hamiltonian preserving integrability. More precisely, we use the so-called Jordanian r-matrix to deform the Hamiltonian of the Richardson-Gaudin model. In order to preserve its integrability, we need to insert a special nilpotent term into the auxiliary L-operator which generates integrals of motion of the system. Moreover, the quantum inverse scattering method enables us to construct the exact eigenstates of the deformed Hamiltonian. These states have a highly complex entanglement structure which require further investigation.
s l 2 Gaudin model with jordanian twist is studied. This system can be obtained as the semiclassical limit of the XXX spin chain deformed by the jordanian twist. The appropriate creation operators that yield the Bethe states of the Gaudin model and consequently its spectrum are defined. Their commutation relations with the generators of the corresponding loop algebra as well as with the generating function of integrals of motion are given. The inner products and norms of Bethe states and the relation to the solutions of the Knizhnik-Zamolodchikov equations are discussed.
Integrable systems take a special niche in quantum many-body systems. Due to the underlying algebraic structure, it is possible to capture all the quantum correlations exactly within a Bethe Ansatz wavefunction at a favourably scaling computational cost. Richardson [1] and Gaudin [2] have shown that the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian of superconductivity [3] is integrable and that the Bethe Ansatz state corresponds to a product wave function of generalized Cooper pairs [4]. In this formulation, the Bethe ansatz state is equivalent to a non-orthogonal geminal, which is widely used in quantum chemistry to describe electron pair correlations in atoms and molecules [5]. Inspired by Richardson-Gaudin integrable systems, it is possible to construct classes of non-orthogonal geminals, allowing for an accurate description of realistic and non-integrable strongly correlated atoms and molecules, while retaining the favorable computational scaling [6, 7]. In this contribution, I will discuss Richardson-Gaudin integrability and why it is useful for strongly correlated systems.
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.