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The quantum phase diagram for the spin-S case of Model-II. The line K = −J/S(2S+1) is an exact first order phase boundary of the FM state, and also the line J = 0 for K < 0.
Source publication
Two quantum spin models with bilinear-biquadratic exchange interactions are
constructed on the checkerboard lattice. It is proved that, under certain
sufficient conditions on the exchange parameters, their ground states consist
of two degenerate Shastry-Sutherland singlet configurations. The constructions
are studied for arbitrary spin-S. The suffi...
Contexts in source publication
Context 1
... Phase Diagram : The approximate quan- tum phase diagrams for spin-1/2 and spin-S cases of Model-II are shown in Figs. 5 and 6. The variational energy per plaquette of H II in the Néel AFM state is : ε II (Néel) = −4S 2 J + KS 2 (2S+1) 2 . Comparing ε II (Néel) with the FM ground state energy (ε II (FM) = 4S 2 J + KS 2 (2S+1) 2 ) gives variational boundary, J = 0, in the region, K < 0. Incidentally, J = 0 (for K < 0) is also an exact sufficient bound for the FM ground state. Therefore, J = 0 is an exact first order phase boundary between the FM and the AFM ground states for K < 0. This is unlike what we saw for Model-I, where we could FM (Exact) 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 only give bounds on the transition region between the FM and and AFM ...
Context 2
... brief remark about the classical spins. In this case (with an appropriate rescaling of K → K/S 2 ), there is no SS phase. Instead, the zero energy sector has a huge classical degeneracy (which is typical of a frustrated clas- sical antiferromagnet). This degeneracy arises due to the fact that each dimer (in an SS like arrangement) requires to have two oppositely oriented spins, independent of the spins in all other dimers. The shaded area between the SS and the Néel state (in Figs. 4 and 6) will become the region of zero energy states in the classical ...
Citations
... Existing parent Hamiltonians of VBC states are a few, being the paradigmatic models in 1D and 2D the Majumdar-Gosh [12] and Shastry-Sutherland [13] models, respectively. More recently, 2D parent Hamiltonians of different VBCs have been constructed [14][15][16] by using sums of local projectors [17]. However, this method may lead to a GS manifold of various degenerate VBC patterns. ...
... As an example, we construct parent Hamiltonians of the staggered-and the columnar-VBC (sVBC and cVBC) on the square lattice, finding that anisotropic four-spin interactions are required to exactly stabilize the VBC in both cases. Interestingly, the sVBC parent Hamiltonian hosts an exact GS within a finite region of the phase diagram, differently from other parent Hamiltonians where the exact GS is found on a single point [12,[14][15][16]. Upon tuning the anisotropy, the VBC transits to a columnar AF (cAF) phase characterized by a finite magnetization at the columnar wave vector (0, π) through a window of intermediate phases (IPs) characterized by the strong competition of correlations at different characteristic lengths (see Fig. 1). ...
We present a general method to construct translational invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBC). The method is based on a canonical mapping transforming S=1/2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamltonians of the columnar- and the staggered-VBC on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the depart from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (cAF) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-cAF transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions.
We study a frustrated spin-$S$ staggered-dimer Heisenberg model on square lattice by using the bond-operator representation for quantum spins, and investigate the setting in of classical magnetic order with increasing $S$, starting from the staggered-dimer singlet ground state. We find the critical coupling for this quantum phase transition to scale as $1/S(S+1)$. But, for strong enough frustration, we also find the quantum mechanical dimer phase to survive even for large $S$ (classical limit). The inclusion of single-ion anisotropy, however, expectedly suppresses the quantum phase, and helps in establishing the classical order (N\'eel or collinear, in the present study) above a critical value that goes as $1/[S(S+1)]$ for large $S$. Thus, in the large $S$ limit, an infinitesimal amount of anisotropy would suffice to realize the classical behaviour.
We study the competition between antiferromagnetic order and valence-bond-crystal formation in a two-dimensional frustrated spin-1/2 model. The J(1)-J(2) model on the square lattice is further frustrated by introducing products of three-spin projectors which stabilize four dimer-product states as degenerate ground state. These four states are reminiscent of the dimerized singlet ground state of the Shastry-Sutherland model. Using exact diagonalization, we study the evolution of the ground state by varying the ratio of interactions. For a large range of parameters (J(2)greater than or similar to 0.25J(1)), our model shows a direct transition between the valence-bond-crystal phase and the collinear antiferromagnetic phase. For small values of J(2), several intermediate phases appear which are also analyzed.
We present an antiferromagnetic quantum spin-1/2 model on honeycomb lattice.
It has two parts, one of which is the usual nearest-neighbor Heisenberg model.
The other part is a certain multiple spin interaction term, introduced by us,
which is exactly solvable for the ground state. Without the Heisenberg part,
the model has an exact threefold degenerate dimer ground state. This exact
ground state is also noted to exist for the general spin-S case. For the
spin-1/2 case, we further carry out the triplon analysis in the ground state,
to study the competition between the Heisenberg and the multiple spin
interactions. This approximate calculation exhibits a continuous quantum phase
transition from the dimer order to N\'eel order.
