Composite spin models are constructed such that, by varying two parameters, they interpolate between the spin-(1/2 antiferromagnetic Heisenberg chain and a number of spin-1 models. These include the usual Heisenberg model, the integrable spin-1 model, and the model with an exact valence-bond ground state. Finite-chain calculations are performed on the composite spin model to study its criticality, and to find if the integrable spin-1 model is a multicritical point with a finite gap generated away from it. We find indications for an extended gapless region.
We consider in detail the ground-state properties of recently introduced generalized Heisenberg models which can have several spin operators at each site and which interpolate smoothly between Heisenberg chains of different spin lengths. We show that the mappings to field-theoretical models used to describe the critical properties of the Heisenberg model remain valid in the composite-spin model. In models which interpolate between the spin-(1/2 and the spin-1 behavior, these mappings predict an extended singlet phase around the isotropic antiferromagnetic point whenever the models move away from the spin-(1/2 point. Numerical calculations on finite chains seem to confirm the existence of this singlet phase. The phase boundaries are, however, found to be independent of the interpolation parameter, and thus in disagreement with the predictions of the continuum theory, indicating its limitation.
The
T=0 behavior of the antiferromagnetic, nearest-neighbor, spin-1 chain is studied in a space of interactions which includes exchange anisotropy, bond alternation, and biquadratic exchange. We find that bond alternation can stabilize N\'eel order; that with sufficient biquadratic coupling the ground state may be spontaneously dimerized and simultaneously critical; and that there is a line of multicritical points where the N\'eel-ordered phase touches the manifold of isotropic coupling. Predictions of Affleck and Haldane regarding the criticality and ordering in these models are tested.
A family of one-dimensional magnetic Hamiltonians is introduced, where at each site there are
n spin-
S operators. It is shown that, for special couplings between spins and for
S=21, the model contains the complete spectrum of the Heisenberg chain with spins \textonehalf{}, 1, frac32;, etc., and the ground state is that of the corresponding Heisenberg chain. By the varying of a single parameter the model allows continuous transitions between chains with different spin. We map the spin-(
S+S) model onto the nonlinear $\ensuremath{\sigma}$ model and discuss the possibility of a finite gap in the spin-(\textonehalf{}+\textonehalf{}) model.
The zero-temperature phase diagram of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N)$ antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general
N. A fully gapped
SU(N) valence bond solid made of
N sites is formed above a critical value of
J2/J1 for all
N. We find that the extension of this
N-merized phase for larger values of
J2 strongly depends on the parity of
N. For even
N, the phase smoothly interpolates to the large
J2 regime where the model can be viewed as a zigzag
SU(N) two-leg spin ladder. The phase exhibits both a
N-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the
N-merized phase with odd
N has only a finite extent with no incommensuration. A gapless phase in the
SU(N)1 universality class is stabilized for larger
J2 that stems from the existence of a massless renormalization group flow from
SU(N)2 to
SU(N)1 conformal field theories when
N is odd.
Using exact numerical diagonalizations as well as the semiclassical spin-wave approach, we study the quantum phase diagram of the spin-12 Heisenberg kagome strip, which is a particular cut-out from the kagome lattice. The unit cell contains five spins placed on the central cite and on the four end sites building two spin-12 along the strip. The model can be characterized by three different constants for the nearest-neighbor exchange bonds between (i) the central and chain spins (J1), (ii) the end spins in a cluster (J2 > 0), and (ii) the spins of neighboring clusters (J′2>0) In the present work we extend the previous studies of the model, which were restricted to antiferromagnetic J1 bonds (J1 > 0), by including the region with ferromagnetic J1 couplings (J1<0). It is demonstrated that for dominating ferromagnetic J1 couplings there is another gapless phase, which can be related to the critical ground state of the spin-52 Heisenberg chain. The phase boundaries separating the discussed critical phases, as well as the behavior of their low-lying excitations close to these boundaries, are examined as well.
The ground-state and thermodynamic properties of quantum mixed-spin chains of 1/2-1/2-1-1 and 3/2-3/2-1-1 are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameter .