title: Quantum fidelity for degenerate ground states in quantum phase transitions.
abstract: Spontaneous symmetry breaking in quantum phase transitions leads to a system having degenerate ground states in its broken-symmetry phase. In order to detect all possible degenerate ground states for a broken-symmetry phase, we introduce a quantum fidelity defined as an overlap measurement between a system ground state and an arbitrary reference state. If a system has N-fold degenerate ground states in a broken-symmetry phase, the quantum fidelity is shown to have N different values with respect to an arbitrarily chosen reference state. The quantum fidelity then exhibits an N-multiple bifurcation as an indicator of a quantum phase transition without knowing any detailed broken symmetry between a broken-symmetry phase and a symmetry phase as a system parameter crosses its critical value (i.e., a multiple bifurcation point). Each order parameter, characterizing a broken-symmetry phase from each degenerate ground state reveals an N-multiple bifurcation. Furthermore, it is shown that it is possible to specify how each order parameter calculated from degenerate ground states transforms under a subgroup of a symmetry group of the Hamiltonian. Examples are given through study of the quantum q-state Potts models with a transverse magnetic field by employing tensor network algorithms based on infinite-size lattices. For any q, a general relation between the local order parameters is found to clearly show the subgroup of the Z_{q} symmetry group. In addition, we systematically discuss criticality in the q-state Potts model.
authors.affiliation: Centre for Modern Physics and Department of Physics, Chongqing University, Chongqing 400044, China and School of Science, Xi'an Polytechnic University, Xi'an 710048, China.
authors.forename: Yao Heng
authors.initials: YH
authors.lastname: Su
authors.forename: Bing-Quan
authors.initials: BQ
authors.lastname: Hu
authors.forename: Sheng-Hao
authors.initials: SH
authors.lastname: Li
authors.forename: Sam Young
authors.initials: SY
authors.lastname: Cho