Abstract
An integrable system is introduced, which is a generalization of the mathfrak{sl} (2) quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated using the ODE/IQFT approach. The model fits into the framework of Yang-Baxter integrability. This opens a way for the systematic quantization of a large class of integrable non-linear sigma models. There may also be some interest in terms of Condensed Matter applications, as the theory can be thought of as a multiparametric generalization of the Kondo model.
Highlights
Suppose we are a given a set of quantum spins S(a) = S1(a), S2(a), S3(a) : SA(a), SB(b) = i δab εABC SC(a), S(a) 2 = ja(ja + 1) (1.1)with a = 1, . . . , r
The model fits into the framework of Yang-Baxter integrability. This opens a way for the systematic quantization of a large class of integrable non-linear sigma models
Among the operators which commute with the transfer-matrix, a special role belongs to the local Integrals of Motion (IM) [4]
Summary
There is a link between the spectrum of the Gaudin Hamiltonians and a class of differential equations possessing certain monodromy properties This provides, perhaps, one of the simplest illustrations of a broad phenomena, known as the ODE/IQFT correspondence [8,9,10,11].2. [5] Feigin and Frenkel introduce the Hamiltonians, which can be interpreted as an “affinization” of H(a) (1.2) They are built from r independent copies of the affine Kac-Moody slka(2) algebra at levels ka = 1, 2, . Feigin and Frenkel put forward the conjecture that the spectrum of these operators would be encoded in a class of differential equations that generalizes (1.7), though they did not explain exactly how the spectrum would be extracted from the ODEs. The last point was clarified in refs.
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