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Bulletin of the American Physical Society

Effective field theory, edge states and classification of symmetric Z2 spin liquids

Yuan-Ming Lu, Ashvin Vishwanath

Published Mar 5, 2014• 0 citations
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Edge states of (2+1)D(2+1)D(2+1)D BFBFBF theory as the effective field theory of translational invariant Z2{\bf Z}_{2}Z2​ spin liquids
Projective symmetry group classification of Z2Z_2Z2​ spin liquids in a pyrochlore lattice
Classification of Z2Z_2Z2​ spin liquids in a hyperkagome lattice by projective symmetry groups
We study possible gapless edge states of translation-symmetric Z2{\mathbb{Z}}_{2}Z2​ spin liquids. The gapless edge states emerge from dangling Majorana fermions at the boundary. We construct a series of mean-field Hamiltonians of Z2{\mathbb{Z}}_{2}Z2​ spin liquids on the square lattice; these models can be obtained by generalization of Wen's exactly solvable plaquette model. We also study the details of the edge theory of these Z2{\mathbb{Z}}_{2}Z2​ spin liquids and find their effective background field (BF) theory descriptions. The effective BF theories are shown to describe the crystal momenta of the ground states and their degeneracies and to predict the edge theories of these Z2{\mathbb{Z}}_{2}Z2​ spin liquids. As a by-product, we obtained a way to classify the BF theories reflecting the lattice symmetries. We discuss in closing three-dimensional Z2{\mathbb{Z}}_{2}Z2​ spin liquids with gapless surface states on the cubic lattice.
Realization of symmetry classes for gapped Z2Z_{2}Z2​ spin liquids in simple models