  Invariance under Lorentz transformations is fundamental to both the standard
model and general relativity. Testing Lorentz-symmetry violation (LSV) via
atomic systems attracts extensive interests in theory and experiment. Some
recent proposals for testing LSV present that the effects of violation can be
described as a local interaction. Further, the test precision of LSV can be
enhanced via quantum entanglement and its quantum Fisher information (QFI)
implicates that the test precision can asymptotically reach the Heisenberg
limit. In general, the limited resolution of collective observables prevents
the detection of large QFI. Here, we propose a multimode many-body quantum
interferometry for testing the LSV parameter $\kappa$ via an ensemble of spinor
atoms. By employing an $N$-atom multimode GHZ state, the test precision can
attain the Heisenberg limit $\Delta \kappa \propto 1/(F^2N)$ with the spin
length $F$ and the atomic number $N$. We find an actual observable (or
practical measurement process) to achieve the ultimate precision and study the
LSV test via an experimentally accessible three-mode interferometry with Bose
condensed spin-1 atoms for example. By selecting suitable input states and
unitary recombination operation, the LSV parameter $\kappa$ can be extracted
via population measurement. Especially, the measurement precision of the LSV
parameter $\kappa$ can beat the standard quantum limit and even approach the
Heisenberg limit via spin mixing dynamics or driving through quantum phase
transitions.
  Our proposed scheme may open up a feasible way for a drastic improvement of
the LSV tests with atomic systems and provide an alternative application of
multi-particle entangled states.
