Gapless deconfined phase in aℤ𝑁-symmetric Hamiltonian created in a cold-atom setup

We investigate a quasi-two-dimensional system consisting of two species of alkali atoms confined in a specific optical lattice potential [Phys. Rev. A 95, 053608 (2017)]. In the low-energy regime, this system is governed by a unique ℤ𝑁 gauge theory, where field theory arguments have suggested that it may exhibit two exotic gapless deconfined phases, namely a dipolar liquid phase and a Bose liquid phase, along with two gapped (confined and deconfined) phases. We address these predictions numerically by using large-scale density matrix renormalization group simulations. Our findings provide conclusive evidence for the existence of a gapless Bose liquid phase for 𝑁≥7. We demonstrate that this gapless phase shares the same critical properties as one-dimensional critical phases, resembling weakly coupled chains of Luttinger liquids. In the range of ladder and cylinder geometries and 𝑁 considered, the gapless dipolar phase predicted theoretically is still elusive and its characterization will probably require a full two-dimensional treatment.