Kumar, Brijesh (2002) Quantum spin models with exact dimer ground states. In: Physical Review B: Condensed Matter and Materials Physics, 66 (2). 024406- .
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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 separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground-state configuration of all the members of the family on a periodic chain. The ground state is twofold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh Hamiltonian with a twofold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to The American Physical Society.|
|Department/Centre:||Division of Physical & Mathematical Sciences > Physics|
|Date Deposited:||28 Jul 2011 10:12|
|Last Modified:||28 Jul 2011 10:12|
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