Quantum phase transitions in matrix product states of one-dimensional spin-½ chains

For the matrix product system of a one-dimensional spin-½ chain, we present a new model of quantum phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψ a 〉 = |1...1〉 representing all particles spin up and |Ψ b 〉 = |0...0〉 representing all particles spin down, while the phase transition point is an isolated intermediate-coupling point where the two phases coexist equally, which is described by the so-called N -qubit maximally entangled GHZ state . At the critical point, the physical quantities including the entanglement are not discontinuous and the matrix product system has long-range correlation and N -qubit maximal entanglement. We believe that our work is helpful for having a comprehensive understanding of quantum phase transitions in matrix product states of one-dimensional spin chains and of potential directive significance to the preparation and control of one-dimensional spin lattice models with stable coherence and N -qubit maximal entanglement.