Exact dimer ground states for a continuous family of quantum spin chains

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.Comment: 11 page

Matrix product states and exactly solvable spin 1/2 Heisenberg chains with nearest neighbor interactions

Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in compact form. The ground state has a very interesting property: all the pairs of spins are equally entangled with each other. Therefore it is possible to engineer long-range entanglement in experimentally realizable spin systems on the one hand and study more closely quantum phase transition in such systems on the other.Comment: 4 pages, RevTex, references added, improved presentation, typos fixe