Emergent fractons and algebraic quantum liquid from plaquette melting transitions

TL;DR

The work reveals that defects of valence plaquette solids are fractons with restricted mobility, leading to a two-stage melting scenario where dipole condensation precedes single-vortex condensation. By mapping VPS to symmetric tensor gauge theories, it predicts a robust 2D algebraic bond liquid (a Bose-surface phase) and outlines its characteristic signatures, including anisotropic dipole correlations, a Bose-surface structure factor, and unusual thermodynamics and entanglement scaling. It further extends these ideas to 3D, where fracton dynamics persist in valence cube/plaquette arrangements and can yield reduced-dimension critical behavior under anisotropy. These results illuminate non-Landau transitions and offer concrete diagnostics for fracton-driven melting and intermediate phases in quantum spin systems.

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 Néel 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.

Figures (11)

• Figure 1: A typical VBS order on a square lattice. When mapping the dimer order to a compact U(1) gauge theory, the magnetic flux operator flips local VBS configurations.
• Figure 2: VBS vortex with a spinon inside the vortex core. The spinon can fluctuate locally by VBS pattern reconstruction. This implies the spinon current carries a gauge charge with respect to the VBS order.
• Figure 3: Left: VPS order which enlarges the unit cell by 4. Right: The vortex connecting four distinct VPS patterns carries a spinon.
• Figure 4: The spinon inside the VPS vortex has restricted mobility. It cannot move without breaking additional plaquettes.
• Figure 5: A dipole can move along the stripe transverse to the dipole's orientation by exchanging position with a plaquette.