Gapless deconfined phase in a $\mathbb{Z}_N$ symmetric Hamiltonian created in a cold-atom setup

TL;DR

This study numerically confirms the existence of a gapless Bose liquid phase in a $ ext{Z}_N$ gauge theory realized in a cold-atom setup, revealing its critical properties and highlighting the challenges in observing the dipolar phase.

Contribution

First numerical evidence of a gapless Bose liquid phase in a $ ext{Z}_N$ gauge theory for $N \,\geq\, 7$ using DMRG simulations, connecting it to Luttinger liquid behavior.

Findings

Confirmed gapless Bose liquid phase for N ≥ 7

Demonstrated critical properties similar to Luttinger liquids

Dipolar phase remains elusive in current geometries

Abstract

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 $\mathbb{Z}_N$ 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 $N \geq 7$. 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.