Quantum deformed Richardson-Gaudin model

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Nyckelord

Eigenstates

Nilpotent

Pairing correlations

Quantum groups

Integrability

Inverse scattering methods

Integrals of motion

Finite chains

Eigenstates; Finite chains; Integrability; Integrals of motion; Inverse scattering methods; Nilpotent; Pairing correlations; Quantum groups

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