  We study Lorentz violation effects on flavor transitions of high energy
astrophysical neutrinos. It is shown that the appearance of Lorentz violating
Hamiltonian can drastically change the flavor transition probabilities of
astrophysical neutrinos. Predictions of Lorentz violation effects on flavor
compositions of astrophysical neutrinos arriving on Earth are compared with
IceCube flavor composition measurement which analyzes astrophysical neutrino
events in the energy range between $25~{\rm TeV}$ and $2.8~{\rm PeV}$. Such a
comparison indicates that the future IceCube-Gen2 will be able to place
stringent constraints on Lorentz violating Hamiltonian in the neutrino sector.
We work out the expected sensitivities by IceCube-Gen2 on dimension-$3$ CPT-odd
and dimension-$4$ CPT-even operators in Lorentz violating Hamiltonian. The
expected sensitivities can improve on the current constraints obtained from
other types of experiments by more than two orders of magnitudes for certain
range of the parameter space.
