Pinch-line spin liquids as layered Coulomb phases and applications to cubic models

Abstract

Spin liquids form fluctuating magnetic textures which have to obey certain rules imposed by frustration. These rules can often be written in the form of a Gauss law, indicating the local conservation of an emergent electric field. In reciprocal space, these emergent Gauss laws appear as singularities known as pinch points, that are accessible to neutron-scattering measurements. But more exotic forms of electromagnetism have been stabilized in spin liquids, and in a few rare instances, these zero-dimensional singularities have been extended into one-dimensional pinch lines. Here we propose a simple framework for the design of pinch-line spin liquids in a layered structure of two-dimensional algebraic spin liquids. A plethora of models can be build within this framework, as exemplified by several concrete examples where our theory is confirmed by simulations, and where the rank of the tensorial gauge field is continuously varied along the pinch line, opening new avenues in fractonic matter. Then we use our framework to understand how the evolution of the singularity pinch point along the pinch line can be understood as the interference pattern of two emergent electric fields. Finally, we apply our intuition on these emergent electric fields in real space to generic pinch line models beyond our layered framework, and revisit the recently proposed pinch line model on the octochlore lattice.

22 pages, 16 figures

References in corpus (12)

• Local stabilizer codes in three dimensions without string logical operators
• Dynamical crystallization in a low-dimensional Rydberg gas
• Continuous Symmetry Breaking in a Two-dimensional Rydberg Array
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Quantum effects on unconventional pinch point singularities
• Combined approach to analyze and classify families of classical spin liquids
• Symmetry fractionalization in the gauge mean-field theory of quantum spin ice
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• Fragmented spin ice and multi-$k$ ordering in rare-earth antiperovskites
• Classification of Classical Spin Liquids: Topological Quantum Chemistry and Crystalline Symmetry

Cited by in corpus (2)

• Decorated cluster lattices: a natural framework for classical spin liquids and flat bands
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice