Quantum phase transitions and bifurcations: reduced fidelity as a phase transition indicator for quantum lattice many-body systems

We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking order. Our finding is based on the observation that in the conventional Landau?Ginzburg?Wilson paradigm a quantum system undergoing a phase transition is characterized in terms of spontaneous symmetry breaking that is captured by a local-order parameter, which in turn results in an essential change of the reduced density matrix in the symmetry-broken phase. Two quantum systems on an infinite lattice in one spatial dimension, i.e. a quantum Ising model in a transverse magnetic field and a quantum spin-1/2 XYX model in an external magnetic field, are considered in the context of the tensor network algorithm based on the matrix product state representation.