The spectrum of a one-dimensional chain of SU(n) spins positioned at the static equilibrium positions of the particles in the corresponding classical Calogero system with an exchange interaction inversely proportional to the square of their distance is studied. As in the translationally invariant Haldane-Shastry model the spectrum is found to exhibit a very simple structure containing highly degenerate 'super-multiplets'. The algebra underlying this structure is identified and several sets of raising and lowering operators are given explicitly. On the basis of this algebra and numerical studies the authors give the complete spectrum and thermodynamics of the SU(2) system.
We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.
We investigate a family of spin-
S chain Hamiltonians recently introduced by one of us [Greiter, Mapping of Parent Hamiltonians, Springer Tracts in Modern Physics, Vol. 244 (Springer, Berlin, 2011)]. 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.
The exact and complete set of highest-weight eigenstates of the finite-size SU(n) Heisenberg chain with inverse-square exchange (ISE) are constructed using the occupation-number representation of the ``strings,'' which can be considered as the unbroken resonating-valence bonds. The string description, which is believed to be exact only in the thermodynamic limit for the Bethe ansatz solvable models, becomes exact for any size ISE model due to the squeezing effect of the strings in the ISE limit. This feature provides a basis for the realization of the Yangian symmetry in the ISE model.
The spectrum and partition function of a model consisting of SU(n) spins positioned at the equilibrium positions of a classical Calogero model and interacting through inverse–square exchange are derived. The energy levels are equidistant and have a high degree of degeneracy, with several SU(n) multiplets belonging to the same energy eigenspace. The partition function takes the form of a q– deformed polynomial. This leads to a description of the system in terms of an effective parafermionic hamiltonian, and to a classification of the states in terms of “modules ” consisting of base–n strings of integers.
Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin
S for the Heisenberg chain with a three-site term $({\mathbf{S}}_{i\ensuremath{-}1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{i})({\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{i+1})+\text{H.c.}$, we use density-matrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for
S=1,
3/2, and 2. The resulting central charge and critical exponent are in good agreement with the
SU(2)k=2S Wess-Zumino-Witten values
c=3k/(2+k) and $\ensuremath{\eta}=3/(2+k)$. Since the three-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that
SU(2)k>1 Wess-Zumino-Witten models might finally be realized in actual spin chains.