Nonlinear Response in Quantum Spin Glasses

We examine the behavior of the dynamic nonlinear response of a quantum spin glass in an exactly solvable fully connected quantum spherical model with random Gaussian bond distribution. In the quantum critical regime where the microscopic energy scale is set entirely by temperature the nonlinear response was found frequency independent and nonsingular. On the contrary, the genuine static nonlinear susceptibility diverges everywhere on the critical boundary with unusual violation of the universal scaling by the double logarithms at the zero-temperature critical point. Implications for experiments on quantum dipolar spin glasses are also noted.