Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2007-05-02
Phys. Rev. B 76, 064433 (2007).
Physics
Condensed Matter
Strongly Correlated Electrons
11 pages
Scientific paper
10.1103/PhysRevB.76.064433
Using the matrix product formalism, we define a multi-parameter family of spin models on one dimensional chains, with nearest and next-nearest neighbor anti-ferromagnetic interaction for which exact analytical expressions can be found for its doubly degenerate ground states. The family of Hamiltonians which we define, depend on 5 continuous parameters and the Majumdar-Ghosh model is a particular point in this parameter space. Like the Majumdar-Ghosh model, the doubly degenerate ground states of our models have a very simple structure, they are the product of entangled states on adjacent sites. In each of these states there is a non-zero staggered magnetization, which vanishes when we take their translation-invariant combination as the new ground states. At the Majumdar-Ghosh point, these entangled states become the spin-singlets pertaining to this model. We will also calculate in closed form the two point correlation functions, both for finite size of the chain and in the thermodynamic limit.
Asoudeh Marzieh
Karimipour Vahid
Sadrolashrafi A.
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