The Existence of Featureless Paramagnets on the Square and the Honeycomb Lattices in 2+1D

Abstract

The peculiar features of quantum magnetism sometimes forbid the existence of gapped `featureless' paramagnets which are fully symmetric and unfractionalized. The Lieb-Schultz-Mattis theorem is an example of such a constraint, but it is not known what the most general restriction might be. We focus on the existence of featureless paramagnets on the spin-1 square lattice and the spin-1 and spin-1/2 honeycomb lattice with spin rotation and space group symmetries in 2+1D. Although featureless paramagnet phases are not ruled out by any existing theorem, field theoretic arguments disfavor their existence. Nevertheless, by generalizing the construction of Affleck, Kennedy, Lieb and Tasaki to a class we call `slave-spin' states, we propose featureless wave functions for these models. The featureless-ness of the spin-1 slave-spin states on the square and honeycomb lattice are verified both analytically and numerically, but the status of the spin-1/2 honeycomb state remains unclear.

11 pages, 16 figures, Added additional references

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• Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
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• Field theory of symmetry-protected valence bond solid states in (2+1) dimensions
• SU(3) quantum critical model emerging from a spin-1 topological phase
• Global anomaly matching in higher-dimensional ${\mathbb{CP}}^{N-1}$ model
• Classification of trivial spin-1 tensor network states on a square lattice
• Classification of symmetry-enriched topological quantum spin liquids
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Possible phases of the spin-$1/2$ $XXZ$ model on a honeycomb lattice by boson-vortex duality