Effect of random fluctuations on quantum spin-glass transitions at zero temperature

We study the effects of random fluctuations on quantum phase transitions by the energy gap analysis. For the infinite-ranged spin-glass models with a transverse field, we find that a strong sample-to-sample fluctuation effect leads to broad distributions of the energy gap. As a result, the linear, spin-glass, and nonlinear susceptibilities behave differently from each other. The power-law tail of the distribution implies a quantum Griffiths-like effect that could be observed in various random quantum systems. We also discuss the mechanisms of the phase transition in terms of the energy gap by comparing the Sherrington-Kirkpatrick model and random energy model, which demonstrate the difference between the continuous and discontinuous phase transitions.