Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary

TL;DR

This paper establishes a correspondence between quantum supersymmetric Gaudin models with boundary and classical Calogero-Moser systems, linking their spectra and classical action variables.

Contribution

It extends the duality between quantum Gaudin models with boundary and classical integrable systems to supersymmetric gl(1|1) cases, revealing new spectral relationships.

Findings

Quantum Hamiltonian spectra match classical particle velocities.

Spectra correspond to the zero level of classical action variables.

Extension of duality to supersymmetric models with boundary.

Abstract

We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras $B_N$, $C_N$, $D_N$ to the case of supersymmetric ${\rm gl}(m|n)$ Gaudin models with $m+n=2$. Namely, we show that the spectra of quantum Hamiltonians for all such magnets being identified with the classical particles velocities provide the zero level of the classical action variables.