Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain

TL;DR

This paper investigates the continuum limit of an integrable superspin chain, revealing a continuous spectrum of conformal weights and suggesting a non-compact target space, with implications for conformal field theory and quantum Hall systems.

Contribution

It provides the first detailed analysis of the continuum limit of the sl(2/1) superspin chain, discovering new features like infinite degeneracies and proposing a connection to the SU(2/1) WZW model.

Findings

Continuous spectrum of conformal weights observed.

Infinite degeneracies in scaled gaps in the thermodynamic limit.

The continuum limit differs from the known model for the spin quantum Hall effect.

Abstract

By a combination of analytical and numerical techniques, we analyze the continuum limit of the integrable 3\otimes\bar{3}\otimes 3\otimes\bar{3}... sl(2/1) superspin chain. We discover profoundly new features, including a continuous spectrum of conformal weights, whose numerical evidence is infinite degeneracies of the scaled gaps in the thermodynamic limit. This indicates that the corresponding conformal field theory has a non compact target space (even though our lattice model involves only finite dimensional representations). We argue that our results are compatible with this theory being the level k=1, `SU(2/1) WZW model' (whose precise definition requires some care). In doing so, we establish several new results for this model. With regard to potential applications to the spin quantum Hall effect, we conclude that the continuum limit of the 3\otimes\bar{3}\otimes 3\otimes\bar{3}... sl(2/1) integrable superspin chain is {\sl not} the same as (and is in fact very different from) the continuum limit of the corresponding chain with two-superspin interactions only, which is known to be a model for the spin quantum Hall effect. The study of possible RG flows between the two theories is left for further study.