Exact Dimer Research Articles

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.

Hole dynamics and photoemission in at−Jmodel forSrCu2(BO3)2

The motion of a single hole in a $t\ensuremath{-}J$ model for the two-dimensional spin-gap compound ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ is investigated. The undoped Heisenberg model for this system has an exact dimer eigenstate and shows a phase transition between a dimerized and a N\'eel phase at a certain ratio of the magnetic couplings. We calculate the photoemission spectrum in the disordered phase using a generalized spin-polaron picture. By varying the interdimer hopping parameters we find a crossover between a narrow quasiparticle band regime known from other strongly correlated systems and free-fermion behavior. The hole motion in the N\'eel-ordered phase is also briefly considered.

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.

Long-Ranged Interacting Quantum Spin Chain with Exact Dimer State

One-dimensional S =1/2 and S =1 spin systems with interactions between not only nearest-neighbor pairs of spins but also longer-range pairs are studied. We find the necessary and sufficient conditions between the coupling constants of the interactions under which the dimer state is an eigenstate of the system. We present a sufficient condition of the dimer ground state for extracted Hamiltonians. Properties of the ground state outside the dimer phase are also discussed by means of an analytical way and numerical diagonalizations.

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.

Exact Dimer State of Quantum Spin Chain with Long-Range Interactions

Quantum Heisenberg antiferromagnets in one dimension with long-range interactions are studied; a Hamiltonian which has dimer states composed of nearest-neighbor singlet pairs as eigenstates of the system is obtained. We also obtain sufficient conditions under which the eigenstates are the ground states. We propose a model which is very similar to the Haldane-Shastry model but has the dimer ground states.

Construction of spin models with dimer ground states

A method to construct various s= 1/2 isotropic spin models with exact dimer ground states is proposed. Constructed models are usually of much simpler forms than those produced by the method using Lowdin's projection operators. They include a series of one-dimensional Heisenberg models which consist of linearly decayed exchange interactions and are natural extensions of the Majumdar-Ghosh model. A two-dimensional spin model with four spin interactions is also constructed to have the same spatial symmetry as a simple square lattice.

Exact dimer statistics and characteristic polynomials of cacti lattices

The pruning method developed earlier by one of the authors (K.B.) combined with the operator method is shown to yield powerful recursive relations for generating functions for dimer statistics and characteristic polynomials of cacti graphs and cacti lattices. The method developed is applied to linear cacti, Bethe cacti of any length containing rings of any size, and cyclic cacti of any length and size. It is shown that exact dimer statistics can be done on any cactus lattice.