When Wannier centers jump: Critical points between atomic insulating phases

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 for certain lattices, 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.

27 pages, 10 figures

References in corpus (50)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• "Deconfined" quantum critical points
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Lieb-Schultz-Mattis in Higher Dimensions
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Fragile Topology and Wannier Obstructions
• Deconfined quantum critical points: symmetries and dualities
• On the stability of U(1) spin liquids in two dimensions
• Properties of an algebraic spin liquid on the kagome lattice
• Interacting fermionic topological insulators/superconductors in three dimensions
• Algebraic spin liquid as the mother of many competing orders
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Topological Quadrupolar Semimetals
• Building crystalline topological phases from lower-dimensional states
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Gauging spatial symmetries and the classification of topological crystalline phases
• Boundary-obstructed topological phases
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Band Representations and Topological Quantum Chemistry
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• A theory of deconfined pseudo-criticality
• Lattice Homotopy Constraints on Phases of Quantum Magnets
• Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological phase
• Towards Bootstrapping QED${}_3$
• Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Composite fermi liquids in the lowest Landau level
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Composite fermion duality for half-filled multicomponent Landau Levels
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Erratum: algebraic spin liquid as the mother of many competing orders
• Phase Diagram of the Two-Flavor Schwinger Model at Zero Temperature
• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Conformality and self-duality of $N_f=2$ QED${}_3$
• Topological obstructed atomic limit by annihilating Dirac fermions
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Unnecessary quantum criticality in $SU(3)$ kagome magnets