Quantum phase transitions in matrix product states of one-dimensional spin-(1/2) chains

For the matrix product system of a one-dimensional spin-1/2chain, we present a new model of quantum2 phase transitions and find that in the thermodynamic limit, both sides of the critical point are respectively described by phases |Ψa =|1··· 1> representing all particles spin up and |Ψb =|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 is2 described by the so-called N-qubit maximally entangled GHZ state |Ψpt =21/2/2(|1··· 1> +|0··· 0>). At the critical point,2the physical quantities including the entanglement are not discontinuous and the matrix product system has longrange 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.