Exact Dimer Ground State Research Articles

Magnetization of the antiferromagnetic cactus graph model with an exact dimer ground state

Magnetization of the antiferromagnetic cactus graph model with an exact dimer ground state

Another exact ground state of a two-dimensional quantum antiferromagnet

We present the exact dimer ground state of a quantum antiferromagnet on the maple-leaf lattice. A coupling anisotropy for one of the three inequivalent nearest-neighbor bonds is sufficient to stabilize the dimer state. Together with the Shastry-Sutherland Hamiltonian, we show that this is the only other model with an exact dimer ground state for all two-dimensional lattices with uniform tilings.

Ground-state properties of linear-exchange quantum spin models

We study a class of one-dimensional antiferromagnetic quantum spin-1/2 models using DMRG. The exchange interaction in these models decreases linearly with the separation between the spins, Jij = R − |i − j| for |i − j| < R, where R is a positive integer ⩾2. For |i − j| ⩾ R, the interaction is zero. It is known that all the odd-R models have the same exact dimer ground state as the Majumdar-Ghosh (MG) model. In fact, R = 3 is the MG model. However, for an even R, the exact ground state is not known in general, except for R = 2 (the integrable nearest-neighbor Heisenberg chain) and the asymptotic limit of R in which the MG dimer state emerges as the exact ground state. Therefore, we numerically study the ground-state properties of the finite even-R ≠ 2 models, particularly for R = 4, 6 and 8. We find that, unlike R = 2, the higher even-R models are spin-gapped, and exhibit robust dimer order of the MG type in the ground state. The spin-spin correlations decay rapidly to zero, albeit showing weak periodic revivals.

The ground state of an XXZ chain with asymmetric second-neighbour interactions

The ground state phase diagram of anXXZ chain with asymmetric second-neighbour interactions is studied. We first prove that thismodel has the doubly degenerate exact dimer ground state under some conditions. Then,by using the level spectroscopy method, we calculate the ground state phase diagram andfind that the dependence of the dimer–fluid critical line on the asymmetric interactions ismuch stronger than those of the dimer–Néel critical line and the ferro-fluid first-ordertransition line. In order to understand this result, we analyse eigenvectors ofthe ground state and excitations characterizing each of phases, and show thatonly the doublet excitation can be used to detect the asymmetric interactions.

The extended spin ladder and net models: exact dimer ground state and quantum phase transition

We investigate an extended spin ladder with diagonal frustrated exchanges in a wide parameter regime. By representing the model as a sum of semidefinite positive projection operators, we prove that this model has exactly a dimer ground state. Smoothly changing parameters may lead the model cover several exactly known models. Starting from this ladder model, we proposed two two-dimensional net models with exact ground states. The quantum phase transition of the ground state, due to the change of exchange strengths along perpendicular rungs, is also discussed.

Exact ground state of the generalized three-dimensional Shastry-Sutherland model

We generalize the Shastry-Sutherland model to three dimensions. By representing the model as a sum of the semidefinite positive projection operators, we exactly prove that the model has exact dimer ground state. Several schemes for constructing the three-dimensional Shastry-Sutherland model are proposed.

Direct Evidence for the Localized Single-Triplet Excitations and the Dispersive Multitriplet Excitations inSrCu2(BO3)2

We performed inelastic neutron scattering on the 2D Shastry-Sutherland system SrCu2(11BO3)2 with an exact dimer ground state. Three energy levels at around 3, 5, and 9 meV were observed at 1.7 K. The lowest excitation at 3.0 meV is almost dispersionless with a bandwidth of 0.2 meV at most, showing a significant constraint on a single-triplet hopping owing to the orthogonality of the neighboring dimers. In contrast, the correlated two-triplet excitations at 5 meV exhibit a more dispersive behavior.

Specific heat study of SrCu 2(BO 3) 2

The specific heat measurement of a two-dimensional spin-gap material SrCu 2(BO 3) 2 with an exact dimer ground state was performed in various magnetic fields up to 12 T. Based on an isolated dimer model, we estimated the spin-gap size at zero field to be 35.0 K. The value of the spin gap decreases in proportion to the applied magnetic field, due to the Zeeman splitting of the excited triplet levels.

Two-Dimensional Cuprate SrCu2(BO3)2 with an Exact Dimer Ground State

Two-Dimensional Cuprate SrCu<SUB>2</SUB>(BO<SUB>3</SUB>)<SUB>2</SUB> with an Exact Dimer Ground State

Exact Dimer Ground State of the Two Dimensional Heisenberg Spin SystemSrCu2(BO3)2

The two dimensional Heisenberg model for SrCu_2(BO_3)_2 has the exact dimer ground state which was proven by Shastry and Sutherland almost twenty years ago. The critical value of the quantum phase transition from the dimer state to the N\'{e}el ordered state is determined. Analysis of the experimental data shows that SrCu_2(BO_3)_2 has the dimer ground state but is close to the transition point, which leads to the unusual temperature dependence of the susceptibility. Almost localized nature of the triplet excitations explains the plateaus observed in the magnetization curve.

A New Type of Argument for the Existence of an Exact Dimer Ground State inS=1/2Quantum Heisenberg Spin Systems

A new type of argument for the existence of an exact dimer ground state in a class of S =1/2 quantum Heisenberg spin systems is presented which gives a necessary and sufficient conditions for the existence of an exact dimer ground state in contrast to the previous arguments which give only the sufficient conditions.