Significance Symmetries are increasingly shown to play various key roles determining the possible phases in condensed matter systems. We study bosonic particles (including electron Cooper pairs) living on the vertices of a honeycomb lattice at a density of 1/2 per site. Here the honeycomb symmetries forbid the usual fermionic band insulating state, and the conventional Mott (“strongly interacting”) insulator involves a whole number of particles frozen on each site, suggesting that featureless (fully symmetric) insulators might not exist in this system. Nevertheless, we explicitly construct quantum states and demonstrate that they are examples of featureless insulators on the honeycomb lattice at 1/2 site filling, with a procedure generalizing to lattices with symmorphic symmetry groups.Significance Symmetries are increasingly shown to play various key roles determining the possible phases in condensed matter systems. We study bosonic particles (including electron Cooper pairs) living on the vertices of a honeycomb lattice at a density of 1/2 per site. Here the honeycomb symmetries forbid the usual fermionic band insulating state, and the conventional Mott (“strongly interacting”) insulator involves a whole number of particles frozen on each site, suggesting that featureless (fully symmetric) insulators might not exist in this system. Nevertheless, we explicitly construct quantum states and demonstrate that they are examples of featureless insulators on the honeycomb lattice at 1/2 site filling, with a procedure generalizing to lattices with symmorphic symmetry groups.

arXiv:1207.0498Proceedings of the National Academy of SciencesSep 23, 201348 citations

INTERACTING ELECTRONS ON THE HONEYCOMB LATTICE

Alessandro Giuliani

Mathematical Results in Quantum Mechanics (QMath)May 1, 20110 citations

Featureless quantum insulator on the honeycomb lattice

Panjin Kim, Hyun‐Yong Lee, Shenghan Jiang +5 more

We show how to construct fully symmetric states without topological order on a honeycomb lattice for $S=\frac{1}{2}$ spins using the language of projected entangled pair states. An explicit example is given for the virtual bond dimension $D=4$ . Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking in the proposed wave functions are checked by numerical calculations of the entanglement entropy and various correlation functions. Exponential decay of all correlation functions measured are strongly indicative of the energy gap for the putative parent Hamiltonian of the state. Our work provides the first explicit realization of a featureless quantum state for spin- $\frac{1}{2}$ particles on a honeycomb lattice.We show how to construct fully symmetric states without topological order on a honeycomb lattice for $S=\frac{1}{2}$ spins using the language of projected entangled pair states. An explicit example is given for the virtual bond dimension $D=4$. Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking in the proposed wave functions are checked by numerical calculations of the entanglement entropy and various correlation functions. Exponential decay of all correlation functions measured are strongly indicative of the energy gap for the putative parent Hamiltonian of the state. Our work provides the first explicit realization of a featureless quantum state for spin-$\frac{1}{2}$ particles on a honeycomb lattice.

arXiv:1509.04358Physical review. B./Physical review. BAug 29, 201631 citations

We show how to construct fully symmetric states without topological order on a honeycomb lattice for

S=\frac{1}{2}

spins using the language of projected entangled pair states. An explicit example is given for the virtual bond dimension

D=4

. Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking in the proposed wave functions are checked by numerical calculations of the entanglement entropy and various correlation functions. Exponential decay of all correlation functions measured are strongly indicative of the energy gap for the putative parent Hamiltonian of the state. Our work provides the first explicit realization of a featureless quantum state for spin-

\frac{1}{2}

particles on a honeycomb lattice.