  In this talk, we study a scalar $O(N)$ model with a so-called moat regime --
a regime with negative bosonic wave function renormalization -- using lattice
field theory. For negative bare wave function renormalization, inhomogeneous
condensates are solutions of the classical equations of motions. Using hybrid
Monte Carlo simulations we demonstrate how bosonic quantum fluctuations
disorder the inhomogeneous condensate. Instead, one finds a so-called Quantum
Pion Liquid, where bosonic correlation functions are spatially oscillating, but
also exponentially decaying.
