A(2|1) spectral equivalences and nonlocal integrals of motion

TL;DR

This paper establishes a spectral correspondence between certain Schrödinger equations and supersymmetric quantum integrable models, providing a systematic method to compute nonlocal conserved quantities in the quantum system.

Contribution

It introduces a novel spectral correspondence linking differential equations to quantum integrable models and offers a systematic approach to compute nonlocal integrals of motion.

Findings

Exact form of key objects in quantum integrable models derived from ODE symmetries

Method to compute nonlocal conserved integrals on the vacuum state

Spectral correspondence enhances understanding of quantum-classical links

Abstract

We study the spectral correspondence between a particular class of Schrodinger equations and supersymmetric quantum integrable model (QIM). The latter, a quantized version of the Ablowitz-Kaupp-Newell-Segur (AKNS) hierarchy of nonlinear equations, corresponds to the thermodynamic limit of the Perk-Schultz lattice model. By analyzing the symmetries of the ordinary differential equation (ODE) in the complex plane, it is possible to obtain important objects in the quantum integrable model in exact form, under an exact spectral correspondence. In this manuscript our main interest lies on the set of nonlocal conserved inte- grals of motion associated to the integrable system and we provide a systematic method to compute their values evaluated on the vacuum state of the quantum field theory.