Related papers: Exact ground state on the 3D analogue of the Shast…
We consider a two-dimensional geometrically frustrated integer-spin Heisenberg system that admits an exact ground state. The system corresponds to a decorated square lattice with two coupling constants J1 and J2, and it can be understood as…
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…
The Shastry-Sutherland model, which consists of a set of spin 1/2 dimers on a 2-dimensional square lattice, is simple and soluble, but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between…
Motivated by the on-going investigation of SrCu$_2$(BO$_3$)$_2$ under pressure, we study a variant of the two-dimensional Shastry-Sutherland (SS) spin-1/2 model with two types of dimers. Combined with the frustration of the SS model, this…
Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intra-dimer and Ising inter-dimer couplings are found by two independent rigorous procedures. The first method uses a unitary…
Extensions of the Shastry-Sutherland model are possible in various ways. In particular, it is possible to construct a natural model in three dimensions which has the exact dimer ground state. Recently found spin gap system SrCu_2(BO_3)_2…
We outline the recent results on the ground state for a class of one- and two-dimensional frustrated quantum spin models with competing ferro(F)- and antiferromagnetic (AF) interactions. Frustrated spin systems are known to have many…
The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when…
Finding an exact solution for a realistic interacting quantum many-body problem is often challenging. There are only a few problems where an exact solution can be found, usually in a narrow parameter space. Here, we propose a spin-$1/2$…
We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized RK points, the exact ground states can be constructed, and ground-state correlation…
Understanding quantum magnetism in two-dimensional systems represents a lively branch in modern condensed-matter physics. In the presence of competing super-exchange couplings, magnetic order is frustrated and can be suppressed down to zero…
Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the…
We have found the exact ground state for two frustrated quantum spin-1/2 models on a linear chain. The first model describes ferromagnet- antiferromagnet transition point. The singlet state at this point has double-spiral ordering. The…
Spin ladders are key models that act as intermediaries between one-dimensional and two-dimensional spin systems. In this study, we examine a coupled spin-$1/2$ ladder, where frustrated ladders with leg, rung, and diagonal interactions are…
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…
The study of interacting spin systems is of fundamental importance for modern condensed matter physics. On frustrated lattices, magnetic exchange interactions cannot be simultaneously satisfied, and often give rise to competing exotic…
We investigate quantum phase transitions of the two-dimensional S=1 Shastry-Sutherland model, which is characterized by the frustrated orthogonal-dimer structure, by means of the exact diagonalization method and the Ising-type series…
We introduce a new two-dimensional model with diagonal four spin exchange and an exactly knownground-state. Using variational ansaetze and exact diagonalisation we calculate upper and lower bounds for the critical coupling of the model.…
We study the spin-$1/2$ two-dimensional Shastry-Sutherland spin model by exact diagonalization of clusters with periodic boundary conditions. We develop an improved level spectroscopic technique using energy gaps between states with…
Inspired by recent experimental measurements [Guo \textit{et al.}, Phys. Rev. Lett.~\textbf{124}, 206602 (2020); Jim\'enez \textit{et al.}, Nature \textbf{592}, 370 (2021)] on frustrated quantum magnet SrCu$_2$(BO$_3$)$_2$ under combined…