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Featureless Quantum Insulator on the Honeycomb Lattice

Shenghan Jiang, Hyun-Yong Lee, Panjin Kim +2 more

Bulletin of the American Physical SocietyMar 14, 20160 citations

Interaction-driven phases in the half-filled honeycomb lattice: An infinite density matrix renormalization group study

Johannes Motruk, Adolfo G. Grushin, Fernando de Juan +1 more

The emergence of the Haldane Chern insulator state due to strong short-range repulsive interactions in the half-filled fermionic spinless honeycomb lattice model has been proposed and challenged with different methods and yet it still remains controversial. In this work we revisit the problem using the infinite density matrix renormalization group method and report numerical evidence supporting (i) the absence of the Chern insulator state, (ii) two previously unnoticed charge ordered phases, and (iii) the existence and stability of all the nontopological competing orders that were found previously within mean field. In addition, we discuss the nature of the corresponding phase transitions based on our numerical data. Our work establishes the phase diagram of the half-filled honeycomb lattice model, tilting the balance towards the absence of a Chern insulator phase for this model.The emergence of the Haldane Chern insulator state due to strong short-range repulsive interactions in the half-filled fermionic spinless honeycomb lattice model has been proposed and challenged with different methods and yet it still remains controversial. In this work we revisit the problem using the infinite density matrix renormalization group method and report numerical evidence supporting (i) the absence of the Chern insulator state, (ii) two previously unnoticed charge ordered phases, and (iii) the existence and stability of all the nontopological competing orders that were found previously within mean field. In addition, we discuss the nature of the corresponding phase transitions based on our numerical data. Our work establishes the phase diagram of the half-filled honeycomb lattice model, tilting the balance towards the absence of a Chern insulator phase for this model.

arXiv:1505.01674Physical Review BAug 26, 201577 citations

Non-equilibrium dynamics of Chern insulators

M. D. Caio, Nigel R. Cooper, Joe Bhaseen

Bulletin of the American Physical SocietyMar 7, 20180 citations

Interaction-driven phases in the half-filled spinless honeycomb lattice from exact diagonalization

N. A. García-Martínez, Adolfo G. Grushin, Titus Neupert +2 more

We investigate the fate of interaction-driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest- and next-nearest-neighbor interactions. We find evidence for a charge density wave phase, a Kekul\'e bond order, and a sublattice charge-modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction-driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground-state degeneracy and by calculating charge-order and bond-order correlation functions.We investigate the fate of interaction-driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest- and next-nearest-neighbor interactions. We find evidence for a charge density wave phase, a Kekul\'e bond order, and a sublattice charge-modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction-driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground-state degeneracy and by calculating charge-order and bond-order correlation functions.

arXiv:1308.6094Physical Review BDec 18, 201371 citations

INTERACTING ELECTRONS ON THE HONEYCOMB LATTICE

Alessandro Giuliani

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

Floquet Fractional Chern Insulators

Adolfo G. Grushin, Álvaro Gómez-León, Titus Neupert

We show theoretically that periodically driven systems with short range Hubbard interactions offer a feasible platform to experimentally realize fractional Chern insulator states. We exemplify the procedure for both the driven honeycomb and the square lattice, where we derive the effective steady state band structure of the driven system by using the Floquet theory and subsequently study the interacting system with exact numerical diagonalization. The fractional Chern insulator state equivalent to the 1/3 Laughlin state appears at 7/12 total filling (1/6 filling of the upper band). The state also features spontaneous ferromagnetism and is thus an example of the spontaneous breaking of a continuous symmetry along with a topological phase transition. We discuss light-driven graphene and shaken optical lattices as possible experimental systems that can realize such a state.We show theoretically that periodically driven systems with short range Hubbard interactions offer a feasible platform to experimentally realize fractional Chern insulator states. We exemplify the procedure for both the driven honeycomb and the square lattice, where we derive the effective steady state band structure of the driven system by using the Floquet theory and subsequently study the interacting system with exact numerical diagonalization. The fractional Chern insulator state equivalent to the 1/3 Laughlin state appears at 7/12 total filling (1/6 filling of the upper band). The state also features spontaneous ferromagnetism and is thus an example of the spontaneous breaking of a continuous symmetry along with a topological phase transition. We discuss light-driven graphene and shaken optical lattices as possible experimental systems that can realize such a state.

arXiv:1309.3571Physical Review LettersApr 18, 2014263 citations

Absence of an interaction driven Chern insulating phase on the honeycomb lattice

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Absence of an interaction driven Chern insulating phase on the honeycomb lattice

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