Emergent fractons and algebraic quantum liquid from plaquette melting transitions

TL;DR

This paper explores how topological defects in valence plaquette solid phases exhibit fracton mobility constraints, leading to novel gapless phases like algebraic bond liquids and providing insights into quantum criticality and exotic quantum liquids.

Contribution

It reveals fracton behavior of topological defects in VPS phases and proposes new gapless phases arising from their melting transitions.

Findings

Defects in VPS phases have fracton mobility constraints.

VPS melting can lead to algebraic bond liquid phases.

Topological defects in 3D VPS also exhibit fractonic dynamics.

Abstract

Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this work, we study the properties of topological defects in valence plaquette solid (VPS) phases on square and cubic lattices. We show that the defects of the VPS order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints deep in the VPS phase, which has been overlooked previously. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist, can potentially inhibit the condensation of vortices and preclude a continuous transition from the VPS to the N\'eel antiferromagnet. Instead, the VPS melting transition can be driven by proliferation of spinon dipoles. For example, we argue that a $2d$ VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long range entanglement. Such a bond liquid phase yields a concrete example of the elusive $2d$ Bose metal with symmetry fractionalization. We also study $3d$ valence plaquette and valence cube ordered phase, and demonstrate that the topological defects therein also have fractonic dynamics. Possible nearby phases after melting the valence plaquettes or cubes are also discussed.