Quantum phase transitions in the Kane-Mele-Hubbard model

Hohenadler, Martin; Meng, Zi Yang; Lang, Thomas C.; Wessel, Stefan; Muramatsu, A.; Assaad, Fakher F.

doi:10.1103/physrevb.85.115132

Cited by 156 publications

(258 citation statements)

References 40 publications

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“…The study of the bulk properties of the Kane-Mele-Hubbard model has attracted considerable attention [96][97][98][99] . Here we focus on the competition between SOC and magnetic order at the edges 40,42,100 .…”

Section: A Kane-mele-hubbard Modelmentioning

confidence: 99%

“…In order to study the interplay between edge magnetism and topologically protected edge states we use the so called Kane-Mele-Hubbard model 40,42,[95][96][97][98][99] Although the gapless edge states are protected against time reversal perturbations, an important issue is whether electron-electron interactions are able to drive the system into a symmetry breaking state. The study of the bulk properties of the Kane-Mele-Hubbard model has attracted considerable attention [96][97][98][99] .…”

Section: A Kane-mele-hubbard Modelmentioning

confidence: 99%

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Edge states in graphene-like systems

2015

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The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are reviewed here. First, zigzag edges host a set of localized non dispersive state at the Dirac energy. At half filling, it is expected that these states are prone to ferromagnetic instability, causing a very interesting type of edge ferromagnetism. Second, graphene under the influence of external perturbations can host a variety of topological insulating phases, including the conventional Quantum Hall effect, the Quantum Anomalous Hall (QAH) and the Quantum Spin Hall phase, in all of which phases conduction can only take place through topologically protected edge states. Here we provide an unified vision of the properties of all these edge states, examined under the light of the same one orbital tight-binding model. We consider the combined action of interactions, spin orbit coupling and magnetic field, which produces a wealth of different physical phenomena. We briefly address what has been actually observed experimentally.

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Section: A Kane-mele-hubbard Modelmentioning

confidence: 99%

Section: A Kane-mele-hubbard Modelmentioning

confidence: 99%

Edge states in graphene-like systems

2015

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“…One of such open questions regards the fate of band electrons in graphene's honeycomb lattice when subject to repulsive interactions at half-filling. The plethora of techniques [4][5][6][7][8] available to study the effect of interactions in this system has produced a range of interesting predictions. In particular, in a series of works, 4,5,9,10 several groups have produced compatible mean-field phase diagrams that suggest that electrons in a honeycomb lattice with extended Hubbard interactions at halffilling stabilize a Chern insulator (CI) phase with topological character and quantized Hall conductivity.…”

Section: Introductionmentioning

confidence: 99%

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

García-Martínez¹,

Grushin²,

Neupert³

et al. 2013

Phys. Rev. B

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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 Kekulé 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.

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“…Kane-Mele-Hubbard model, is an example of such models which recently has been studied by various methods [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] . The strong coupling (large Coulomb interaction) and weak coupling (small Coulomb interaction) limits of this model are charachterized by anti-ferromagnetic Mott insulator (AFMI) and topological band insulator (TBI) phases, respectively.…”

Section: J2 J1mentioning

confidence: 99%

Valence bond phases inS= 1/2 Kane–Mele–Heisenberg model

Zare

Mosadeq

Shahbazi

et al. 2014

J. Phys.: Condens. Matter

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The phase diagram of Kane-Mele-Heisenberg (KMH) model in classical limit 47 , contains disordered regions in the coupling space, as the result of to competition among different terms in the Hamiltonian, leading to frustration in finding a unique ground state. In this work we explore the nature of these phase in the quantum limit, for a S = 1/2. Employing exact diagonalization (ED) in Sz and nearest neighbor valence bond (NNVB) bases, bond and plaquette valence bond mean field theories, We show that the disordered regions are divided into ordered quantum states in the form of plaquette valence bond crystal (PVBC) and staggered dimerized (SD) phases.

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Quantum phase transitions in the Kane-Mele-Hubbard model

Cited by 156 publications

References 40 publications

Edge states in graphene-like systems

Edge states in graphene-like systems

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

Valence bond phases inS= 1/2 Kane–Mele–Heisenberg model

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