Quantum fidelity, string order parameter, and topological quantum phase transition in a spin-1/2 dimerized and frustrated Heisenberg chain

Topological quantum phase transitions are numerically investigated in a spin-1/2 dimerized and frustrated Heisenberg chain by using infinite matrix product state representation with the infinite time evolving block decimation method. Quantum fidelity approach is employed to detect the degenerate ground states and quantum phase transitions. By calculating the long-range string order parameters, we find two topological Haldane phases characterized by two long-range string orders. Also, continuous and discontinuous behaviors of von Neumann entropy show that phase transitions between two topological Haldane phases are topologically continuous and discontinuous quantum phase transitions. For the topologically continuous phase transition, the central charge at the critical point is obtained as c=1, which means that the topologically continuous quantum phase transition belongs to the Gaussian universality class. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015