Unusual critical points between atomic insulating phases

TL;DR

The paper shows that transitions between two trivial (featureless) atomic insulators in $(2+1)$d can realize unconventional critical points described by $N_f=4$ QED$_3$, with stability dictated by how lattice symmetries embed into the IR and by anomaly matching. Through a one-dimensional SSH warm-up and two lattice models (BBH-type on breathing lattices), it demonstrates that monopole proliferation, controlled by lattice symmetry, can render the fixed point unstable (often leading to first-order behavior) on bipartite lattices, whereas tripartite lattices with symmetry-forbidden monopoles support a genuine, stable QED$_3$ critical point. Anomaly matching provides a rigorous consistency check, confirming that these critical theories are emergent from local lattice Hamiltonians, and clarifies how UV lattice symmetries map to IR dynamics. The work suggests a broader paradigm where trivial-to-trivial insulator transitions can host rich critical physics beyond Landau theory, with potential extensions to higher dimensions and experimental realizations.

Abstract

We study a class of quantum phase transitions between featureless bosonic atomic insulators in $(2+1)$ dimensions, where each phase exhibits neither topological order nor protected edge modes. Despite their lack of topology, these insulators may be ``obstructed'' in the sense that their Wannier centers are not pinned to the physical atomic sites. These insulators represent distinct phases, as no symmetry-preserving adiabatic path connects them. Surprisingly, we find that the critical point between these insulators can host a conformally invariant state described by quantum electrodynamics in $(2+1)$ dimensions (QED$_3$). The emergent electrodynamics at the critical point can be stabilized if the embedding of the microscopic lattice symmetries suppresses the proliferation of monopoles, suggesting that even transitions between trivial phases can harbor rich and unexpected physics. We analyze the mechanism behind this phenomenon, discuss its stability against perturbations, and explore the embedding of lattice symmetries into the continuum through anomaly matching. In all the models we analyze, we confirm that the QED$_3$ is indeed emergeable, in the sense that it is realizable from a local lattice Hamiltonian.

Figures (12)

• Figure 1: Two possible atomic insulating phases on the square lattice, tuned by a parameter $\lambda$. In the language of crystallographic space groups, the Wannier centers of the particles move from the $1a$ to the $1d$ Wyckoff positions as $\lambda$ is tuned across the phase transition.
• Figure 2: An illustration of the two phases of the SSH model as the relative strength of the dimerized hoppings is tuned.
• Figure 3: The phase diagram of the SSH chain the presence of interaction. Upon adding interactions, there is a marginal line of non-Fermi liquids separating the two trivial insulating phases. The line terminates at the free fermion critical point in Eq. \ref{['eq:ssh_dirac']}.
• Figure 4: (a) The vanishing of the energy gap, as the critical point is reached. The gap is is linear in $\delta t\sim t-t_*$. (b) Schematic vanishing of the quasiparticle weight as the critical point is approached in the presence of interactions.
• Figure 5: An illustration of the BBH model. There are four orbitals per site, with a $C_4$ symmetric hopping between orbitals and sites. The dashed lines above indicate a negative hopping amplitude, a gauge choice that inserts $\pi$ through each plaquette. Equivalently, one can view the orbitals as sublattice sites and treat the system as a decorated square lattice.