First order quantum phase transitions in the XX spin chain

Quantum phase transitional behavior of a finite periodic XX spin1 2 chain with nearest neighbor interaction in a uniform transverse field is studied based on the simple exact solutions. It is found that there are [N/2] quantum critical points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitions are all of the first order due to level-crossing. The ground state in the thermodynamic limit will be divided into three distinguishable quantum phases with one non-degenerate long-range order phase, one two-fold degenerate continuous long-range order phase and one non-degenerate ferromagnetic phase. It is well known that the finite periodic XX spin1 2 chain with nearest neighbor interaction in a uniform transverse field is simply solvable. The result was first reported by Lieb et al, and then by many others. Similar models have been attracted a lot of attention recently due to the fact that they may be potentially helpful in quantum information processing and realizable by using quantum dots, optical lattice, or spin interaction systems. These spin systems usually undergo quantum phase transitions (QPTs) under certain conditions at zero temperature, which can be characterized by non-analyticity in properties of the ground state. There are intimate links between QPTs and entanglement in the systems. In this Letter it will be shown that there are a series of critical points signaturing a series of first order quantum phase transitions when the interaction strength and magnitude of the magnetic field satisfy certain conditions, and the entanglement measure defined in terms of von Neumann entropy of one-body reduced density matrix can be used to indicating both the multi-particle entanglement and QPTs in the system. The Hamiltonian of the model can be written as