Deformed Richardson-Gaudin model

P Kulish,A Stolin,L H Johannesson

doi:10.1088/1742-6596/532/1/012012

Abstract

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.

Highlights

The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain
Richardson’s exact solution of the model [1], exploiting its integrability, has been important for applications in mesoscopic and nuclear physics where the small number of fermions prohibits the use of conventional BCS theory [4]
The commutation relations (CR) of loop algebra generators are given in compact matrix form

Summary

Introduction

The Richardson-Gaudin model describes strong pairing correlations of fermions confined to a finite chain. The Richardson-Gaudin model [1, 2] is an integrable spin-1/2 periodic chain with Hamiltonian M m the Richardson-Gaudin model in Eq (1) gets mapped onto the pairing model Hamiltonian C†lm (clm) creates (annihilates) a fermion in the state | lm (with | lmthe time reversed state of | lm ), and nl = m c†lmclm and A†l = (Al)† = m c†lmc†lmare the corresponding number- and pair-creation operators.

Results

Conclusion