  Quantum criticality has been demonstrated as a useful quantum resource for
parameter estimation. This includes second-order, topological and localization
transitions. In all these works reported so far, gap-to-gapless transition at
criticality has been identified as the ultimate resource for achieving the
quantum enhanced sensing, although there are several important concepts
associated with criticality, such as long-range correlation, symmetry breaking.
In this work, we analytically demonstrate that symmetry-breaking can drive a
quantum enhanced sensing in single- or multiparameter estimation. We show this
in the well-known Kitaev model, a lattice version of the 1D p-wave
superconductor, which consists of a pairing term and an onsite potential term.
The model is characterized by two critical lines and a multi-critical point at
the intersection of these two lines. We show that Heisenberg scaling can be
obtained in precision measurement of the superconducting coupling by preparing
the system at or near the multicritical point despite the fact that parameter
variation follows the critical lines, i.e., without an explicit requirement of
gap-to-gapless transition. Quantum enhancement in such situations solely occurs
due to a global U(1) symmetry-breaking by the pairing term. Extending our
analysis in the realm of multiparameter estimation we show that it is possible
to obtain super-Heisenberg scaling by combining the effects of
symmetry-breaking and gapless-to-gapped transition.
