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; 85(19). DOI: 10.1103/PhysRevB.85.195149
Source: arXiv

ABSTRACT We investigate a family of spin-S chain Hamiltonians recently introduced by
one of us. For S=1/2, it corresponds to the Haldane-Shastry model. For general
spin S, we find indication that the low-energy theory of these spin chains is
described by the SU(2)_k Wess-Zumino-Witten model with coupling k=2S. In
particular, we investigate the S=1 model whose ground state is given by a
Pfaffian for even number of sites N. We reconcile aspects of the spectrum of
the Hamiltonian for arbitrary N with trial states obtained by Schwinger
projection of two Haldane-Shastry chains.


Available from: Ronny Thomale, May 30, 2015
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S=1 and sigma=1/2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.
    Physics of Condensed Matter 07/2014; 87(10). DOI:10.1140/epjb/e2014-50423-7 · 1.46 Impact Factor
  • Source
    [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.
    Journal of Physics A Mathematical and Theoretical 09/2014; 48(6). DOI:10.1088/1751-8113/48/6/065205 · 1.69 Impact Factor
  • Source
    [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.