  Contrary to the conventional wisdom in Hermitian systems, a continuous
quantum phase transition between gapped phases is shown to occur without
closing the energy gap $\Delta$ in non-Hermitian quantum many-body systems.
Here, the relevant length scale $\xi \simeq v_{\rm LR}/\Delta$ diverges because
of the breakdown of the Lieb-Robinson bound on the velocity (i.e.,
unboundedness of $v_{\rm LR}$) rather than vanishing of the energy gap
$\Delta$. The susceptibility to a change in the system parameter exhibits a
singularity due to nonorthogonality of eigenstates. As an illustrative example,
we present an exactly solvable model by generalizing Kitaev's toric-code model
to a non-Hermitian regime.
