Atomic Insulating Phases Exhibit Critical Points Hosting Conformally Invariant States in Dimensions

The behaviour of materials at phase transitions, where they shift from one state to another, often reveals surprising new physics, and recent work by Yunchao Zhang from the Massachusetts Institute of Technology, and T. Senthil, explores unusual transitions between atomic insulating phases. These phases, while lacking the complex properties of topological materials, can still exhibit subtle obstructions preventing a smooth connection between them, creating a unique situation for study. The researchers demonstrate that the critical point between these seemingly simple insulators can unexpectedly host a conformally invariant state resembling electrodynamics, a fundamental theory governing interactions between light and matter. This discovery challenges the conventional understanding that only topologically ordered phases can give rise to such emergent phenomena, and suggests that even transitions between trivial phases can harbour rich and unexpected physics with potential implications for materials science and condensed matter physics.

These phases, lacking topological order, can be “obstructed”, meaning their fundamental building blocks are not neatly localized on the atomic sites. This obstruction leads to the surprising emergence of gapless boundary modes, conducting pathways at the edges of the material, when the insulating phases undergo a transition, even though the bulk material remains insulating. The critical points governing these transitions exhibit unusual behaviour, deviating from established theories. The research demonstrates that obstruction, distinct from topology, can drive criticality and generate these emergent gapless modes, challenging conventional understandings of quantum phase transitions in condensed matter physics.

These insulating phases are unique because their constituent particles are not pinned to the physical atomic sites, representing distinct states of matter. Surprisingly, the transition point between these insulators hosts a conformally invariant state, behaving like quantum electrodynamics in lower dimensions. This emergent electrodynamics can be stabilized if the arrangement of atoms suppresses the formation of magnetic-like particles called monopoles, suggesting that even transitions between simple phases can exhibit rich and unexpected physics.

Topological Phases and Symmetry Protected States

Research in condensed matter physics increasingly focuses on topological phases of matter, systems exhibiting unusual properties protected by fundamental symmetries. A central theme is the role of symmetry in constraining the possible states of matter and protecting these exotic phases from disruption. Scientists are investigating strongly correlated electron systems, where interactions between electrons are crucial, applying techniques from quantum field theory. Emerging areas of research include non-Hermitian physics and the study of dualities, revealing hidden connections between different physical systems.

A key focus is the interplay between anomalies and topological phases. Anomalies, representing violations of classical symmetries at the quantum level, can protect topological phases by preventing them from decaying. Researchers are exploring symmetry-protected topological phases and more exotic phases that may not be protected by symmetry in the traditional sense, employing quantum field theory methods like renormalization group and effective field theories. The study of fractionalization, where electrons break up into fractionalized quasiparticles with exotic exchange statistics, is also prominent. Researchers are investigating systems exhibiting these properties, such as the fractional quantum Hall effect, using techniques like bosonization and conformal field theory to understand one-dimensional systems and their unique properties. This research represents a sophisticated and interdisciplinary approach to understanding complex materials.

Emergent Electrodynamics at Insulator Transitions

Recent research reveals the surprising emergence of complex physics at the transition points between seemingly simple insulating states of matter. Scientists have discovered that transitions between these insulators, lacking topological properties, can unexpectedly host a conformally invariant state resembling electrodynamics in lower dimensions. The team established that the stability of this emergent electrodynamic behaviour depends critically on the symmetries of the underlying atomic lattice, specifically the suppression of monopole proliferation. Through careful analysis using anomaly matching, they confirmed that these critical theories are indeed realizable within local lattice models, demonstrating a fundamental connection between microscopic lattice structure and macroscopic emergent phenomena.

The researchers acknowledge that their current work focuses on transitions driven by specific mechanisms, such as electrons acquiring mass, and that more general transitions may require different theoretical approaches. Future research directions include exploring these critical points in higher dimensions and investigating transitions arising from different types of band structures. The relative simplicity of the models studied offers the potential for verification through numerical simulations and, potentially, experimental observation.