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Existence of a dipolar gapless liquid in the U(1) thermodynamic limit

Determine whether a gapless dipolar liquid phase exists in the thermodynamic U(1) symmetric limit of the emergent Z_N lattice gauge theory realized from the two-species cold-atom setup, specifically in the combined limit L_x → ∞, g → 0, N → ∞ with gN held constant.

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Background

The paper studies an emergent Z_N lattice gauge theory arising from a two-species ultracold bosonic system and provides numerical evidence for a gapless Bose liquid phase for N ≥ 7 in ladder and cylinder geometries. Field-theoretic arguments had suggested two distinct gapless deconfined phases: a Bose liquid at intermediate coupling and a dipolar liquid in the U(1) limit with gN finite.

While the authors confirm the Bose liquid phase numerically for finite N and quasi-2D geometries, they report that the dipolar liquid phase remains unobserved under their constraints (finite N and limited transverse size). They emphasize that, in the thermodynamic and U(1) limit (L_x → ∞, g → 0, N → ∞, gN = const), the dipolar liquid has been conjectured to exist, and its existence remains an unresolved question within the scope of their paper.

References

On the other hand, we cannot confirm the existence of another gapless (presumably dipolar liquid) phase. As a result, even if we cannot observe it, we cannot exclude the possibility of its existence in the thermodynamic limit of the U(1) symmetric theory where the dipolar liquid phase is conjectured to exist, i.e., in the limit ($L_x\to \infty, g \to 0$, $N \to \infty$, $gN = {\rm const}$).

— Gapless deconfined phase in a $\mathbb{Z}_N$ symmetric Hamiltonian created in a cold-atom setup (2407.12109 - Rakov et al., 16 Jul 2024) in Section 5 (Conclusion)