Itamar Kimchi, S. A. Parameswaran, Ari M. Turner, Ashvin Vishwanath
It is well known that band insulators require an integer number of electrons (of each spin) per unit cell. Similarly, in bosonic insulators where the number of particles per unit cell (f) is fractional, the ground state either enlarges the unit cell, or realizes an exotic topologically ordered (fractionalized) state. Symmetric non-fractionalized Mott insulators only appear at integer f. However, the converse problem is relatively unexplored - is such a symmetric non-fractionalized insulator always allowed at integer f, or can it be prohibited by other lattice symmetries? An especially relevant example is the honeycomb lattice - where free spinless fermions at f=1 (or, 1/2 site filling) are always metallic, due to point group symmetries. Here we argue that bosons at the same filling however can realize a Mott phase. We propose a wave function for this state and by a mapping to a classical partition function we compute its properties and demonstrate that the state is insulating, fully symmetric and has no topological order. Thus the absence of symmetry breaking in this case does not imply topological order. Our construction suggests that featureless insulators are generically allowed for bosons at unit filling on any symmorphic lattice in any dimension.
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http://arxiv.org/abs/1207.0498
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