Reduced-fidelity approach for quantum phase transitions in spin-12dimerized Heisenberg chains

Abstract

We show a general connection between the reduced-fidelity susceptibility and quantum phase transitions, and derive an explicit expression of the reduced-fidelity susceptibility for the one-dimensional spin-1/2 dimerized Heisenberg chain, which has both SU(2) and translational symmetries. We find that the reduced-fidelity susceptibility is directly related to the square of the second derivative of ground-state energy, which means that it is an effective indicator of the second-order quantum phase transitions. In terms of this indicator, we explicitly examine the critical behavior of the spin-1/2 dimerized Heisenberg chain. Moreover, we give another two exemplifications to show that the results may also be extended to high-spin systems.