Table 3 Fermion bilinear and monopole symmetries on the kagome lattice
From: Unifying description of competing orders in two-dimensional quantum magnets
T 1 | T 2 | R y | C 6 | \({\cal{T}}\) | |
|---|---|---|---|---|---|
M 00 | + | + | − | + | − |
M 01 | − | − | −M03 | M 02 | + |
M 02 | + | − | M 02 | −M03 | + |
M 03 | − | + | −M01 | −M01 | + |
M i0 | + | + | − | + | + |
M i1 | − | − | −Mi3 | M i2 | − |
M i2 | + | − | M i2 | −Mi3 | − |
M i3 | − | + | −Mi1 | −Mi1 | − |
\({\mathrm{\Phi }}_1^\dagger\) | \(- {\mathrm{\Phi }}_1^\dagger\) | \(- {\mathrm{\Phi }}_1^\dagger\) | \(-{{\Phi }}\) 3 | \(e^{i\frac{{2\pi }}{3}}{\mathrm{\Phi }}_2^\dagger\) | \({{\Phi }}\) 1 |
\({\mathrm{\Phi }}_2^\dagger\) | \({\mathrm{\Phi }}_2^\dagger\) | \(- {\mathrm{\Phi }}_2^\dagger\) | \({{\Phi }}\) 2 | \(- e^{i\frac{{2\pi }}{3}}{\mathrm{\Phi }}_3^\dagger\) | \({{\Phi }}\) 2 |
\({\mathrm{\Phi }}_3^\dagger\) | \(- {\mathrm{\Phi }}_3^\dagger\) | \({\mathrm{\Phi }}_3^\dagger\) | \(-{{\Phi }}\) 1 | \(- e^{i\frac{{2\pi }}{3}}{\mathrm{\Phi }}_1^\dagger\) | \({{\Phi }}\) 3 |
\({\mathrm{\Phi }}_{4/5/6}^\dagger\) | \({\mathrm{\Phi }}_{4/5/6}^\dagger\) | \({\mathrm{\Phi }}_{4/5/6}^\dagger\) | \(-{{\Phi }}\) 4/5/6 | \(e^{i\frac{{2\pi }}{3}}{\mathrm{\Phi }}_{4/5/6}^\dagger\) | \(-{{\Phi }}\) 4/5/6 |
