Article

# A family of spin-S chain representations of SU(2)_k Wess-Zumino-Witten models

Physical review. B, Condensed matter (Impact Factor: 3.66). 10/2011; DOI: 10.1103/PhysRevB.85.195149

Source: arXiv

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**ABSTRACT:**We construct 1D and 2D long range SU(N) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N) level 1 WZW model. Since the resulting groundstates are of Gutzwiller-Jastrow type, our models can be regarded as lattice discretizations of fractional quantum Hall systems. We then focus on two specific types of 1D spin chains with spins located on the unit circle, a uniform and an alternating arrangement. For an equidistant distribution of identical spins we establish an explicit connection to the SU(N) Haldane-Shastry model, thereby proving that the model is critical and described by a SU(N) level 1 WZW model. In contrast, the alternating model can only be treated numerically but it turns out to be critical as well. Our numerical results rely on a reformulation of the original problem in terms of loop models.Nuclear Physics B. 04/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**We construct 1D and 2D long range SU(N) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N) level 1 WZW model. Since the resulting groundstates are of Gutzwiller-Jastrow type, our models can be regarded as lattice discretizations of fractional quantum Hall systems. We then focus on two specific types of 1D spin chains with spins located on the unit circle, a uniform and an alternating arrangement. For an equidistant distribution of identical spins we establish an explicit connection to the SU(N) Haldane-Shastry model, thereby proving that the model is critical and described by a SU(N) level 1 WZW model. In contrast, the alternating model can only be treated numerically but it turns out to be critical as well. Our numerical results rely on a reformulation of the original problem in terms of loop models.05/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**The six-vertex model and its spin-$S$ descendants obtained from the fusion procedure are well-known lattice discretizations of the SU$(2)_k$ WZW models, with $k=2S$. It is shown that, in these models, it is possible to exhibit a local observable on the lattice that behaves as the chiral current $J^a(z)$ in the continuum limit. The observable is built out of generators of the su$(2)$ Lie algebra acting on a small (finite) number of lattice sites. The construction works also for the multi-critical quantum spin chains related to the vertex models, and is verified numerically for $S=1/2$ and $S=1$ using Bethe Ansatz and form factors techniques.09/2014;

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