  The fidelity susceptibility is a general purpose probe of phase transitions.
With its origin in quantum information and in the differential geometry
perspective of quantum states, the fidelity susceptibility can indicate the
presence of a phase transition without prior knowledge of the local order
parameter, as well as reveal the universal properties of a critical point. The
wide applicability of the fidelity susceptibility to quantum many-body systems
is, however, hindered by the limited computational tools to evaluate it. We
present a generic, efficient, and elegant approach to compute the fidelity
susceptibility of correlated fermions, bosons, and quantum spin systems in a
broad range of quantum Monte Carlo methods. It can be applied both to the
ground-state and non-zero temperature cases. The Monte Carlo estimator has a
simple yet universal form, which can be efficiently evaluated in simulations.
We demonstrate the power of this approach with applications to the Bose-Hubbard
model, the spin-$1/2$ XXZ model, and use it to examine the hypothetical
intermediate spin-liquid phase in the Hubbard model on the honeycomb lattice.
