Quantum Liquids: Emergent higher-rank gauge theory and fractons

TL;DR

This paper reviews gapless fracton liquids, highlighting their emergent higher-rank gauge theories, unique mobility restrictions, and potential material realizations, advancing understanding of their theoretical foundations and experimental prospects.

Contribution

It provides a comprehensive overview of gapless fracton liquids, including emergent tensor gauge theories, their properties, and methods to realize and manipulate them in quantum materials.

Findings

Fracton liquids exhibit collective gauge-like excitations with restricted mobility.

Higher-moment conservation laws distinguish fracton liquids from conventional gauge theories.

Material platforms like Yb-based lattices can realize fracton phases.

Abstract

Fracton emerges from strongly interacting many-body systems whose excitations, referred to as sub-dimensional particles, have restricted mobility or kinetic motions. These entities have garnered significant interest due to their interdisciplinary implications spanning topological quantum codes, quantum field theory, emergent gravity, quantum information, and more, revealing unique nonequilibrium behaviors such as nonergodicity and glassy dynamics. This review presents a structured and educational overview of fracton phenomena, specifically focusing on gapless fracton liquids. Noteworthy for their compressibility and gapless excitations, fracton liquids facilitate collective modes reminiscent of those gauge fluctuations found in Maxwell's electromagnetic framework. However, they are distinct due to an additional higher-moment conservation law that restricts the mobility of individual charges and monopoles. Our exploration begins with the theoretical foundation of 3D fracton liquids, presenting a variety of emergent symmetric tensor gauge theories and reviewing their equilibrium and dynamic properties. Following this theoretical groundwork, we discuss the material realization of various fracton liquids in Yb-based breathing pyrochlore lattices, close-packed tiling structures and other synthetic quantum matter platforms. Additionally, we introduce a general protocol to foster and manipulate emergent fracton spin liquids in the realm of frustrated magnetism.