Deformed Richardson-Gaudin model

3Quantum: Algebra Geometry Information

物理学;数学

Kulish, P.^1 ; Stolin, A.^2 ; Johannesson, L.H.^2

St. Petersburg Department, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St.-Petersburg

191023, Russia^1

University of Gothenburg, Box 100, Gothenburg

SE-405 30, Sweden^2

关键词: Algebraic constructions;    Eigenstates;    Finite chains;    Integrability;    Integrals of motion;    Inverse scattering methods;    Pairing correlations;    Quantum groups;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/532/1/012012/pdf
DOI  :  10.1088/1742-6596/532/1/012012

来源: IOP

【 摘 要 】

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.