Kane-Mele Hubbard model on a zigzag ribbon: Stability of the topological edge states and quantum phase transitions

Chung, Chung-Hou; Lee, Der Hau; Chao, Sung Po

doi:10.1103/physrevb.90.035116

Cited by 10 publications

(3 citation statements)

References 50 publications

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“…There is a significant volume of work especially on nanoribbons using Hubbard and Hubbard-like models [10][11][12] to explore the effect of correlations. The strength of Coulomb interactions in graphene has been clarified recently.…”

Section: Introductionmentioning

confidence: 99%

Exact diagonalization study for nanographene: Modulation of charge and spin, magnetic phase diagram, and thermodynamics

et al. 2014

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We investigate the many-body-instability-driven electronic, magnetic, and thermodynamic properties of graphene nanoflakes described by an extended Hubbard model using exact diagonalization. Our exact results lead to a complete magnetic phase diagram in n-V space, where n is the filling and V is the nonlocal Coulomb interaction. The phase diagram is found to consist of reentrant phases with net magnetic moment, separated by those with zero magnetic moment. The interplay of local and nonlocal Coulomb interaction, geometry, and filling gives rise to complex magnetic phases with coexisting antiferromagnetic and ferromagnetic correlations, of both short-range and long-range nature. A small change in temperature or in the strength of the nonlocal Coulomb interaction is found to drive the change in the magnetic state. The low-temperature thermodynamic behavior, driven by the crossover of eigenstates of contrasting magnetic characters, is signaled by a sharp peak in the specific heat.

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Section: Introductionmentioning

confidence: 99%

Exact diagonalization study for nanographene: Modulation of charge and spin, magnetic phase diagram, and thermodynamics

et al. 2014

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“…6, we turn to the helical Luttinger liquid theory. Based on the space-time rotation interpretation of the strange correlator, we can analyze the single-particle strange correlator using the helical Luttinger liquid theory at the (1+1)D boundary [49][50][51][52] , according to which the real-space strange correlator in the single-particle sector scales as…”

Section: Numerical Results and Discussion A Single-particle Strange C...mentioning

confidence: 99%

Quantum Monte Carlo study of strange correlator in interacting topological insulators

You

et al. 2015

Phys. Rev. B

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Distinguishing the nontrivial symmetry-protected topological (SPT) phase from the trivial insulator phase in the presence of electron-electron interaction is an urgent question to the study of topological insulators, due to the fact that most of the topological indices defined for free electron systems are very likely unsuitable for interacting cases. In this work, we demonstrate that the strange correlator is a sensitive diagnosis to detect SPT states in interacting systems. Employing large-scale quantum Monte Carlo (QMC) simulations, we investigate the interaction-driven quantum phase transition in the Kane-Mele-Hubbard model. The transition from the quantum spin Hall insulator at weak interaction to an antiferromagnetic Mott insulator at strong interaction can be readily detected by the momentum space behavior of the strange correlator in single-particle, spin, and pairing sectors. The interaction effects on the symmetry-protected edge states in various sectors, i.e., the helical Luttinger liquid behavior, are well captured in the QMC measurements of strange correlators. Moreover, we demonstrate that the strange correlator is technically easier to implement in QMC and more robust in performance than other proposed numerical diagnoses for interacting topological states, as only static correlations are needed. The attempt in this work paves the way for using the strange correlator to study interaction-driven topological phase transitions in fermionic as well as bosonic systems.

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“…With even strips implying a zero gap while for odd strips we have a small non-zero gap [21] 1.50 1.55 1.60 1. We now plot the gap for the quasi-1D with 1 to 6 strips, the existence of edge states can be identified when the gap is zero.…”

Section: Quasi-1d Systemsmentioning

confidence: 99%

Impurezas magnéticas no modelo de Kanie-Mele com supercondutividade

Teixeira¹

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In this work, we study a honeycomb lattice with induced superconductivity and edge impurity in order to show the existence of a phase that host Majorana bound state. To do so, we start introducing topological invariants, Chern number and Z 2 , and we show two models for honeycomb lattice. The first, Haldane's Model, due its historical importance. The second, Kane-Mele model[1], because it will be used during all this work. Then we review superconductivity, showing the self-consistent method, and we apply it to Kane-Mele model, in which we find some necessary conditions to induce superconductivity only at the edges. From this point, we study the effect of magnetic impurities at the edges, and we introduce Majorana bound state, that will be the main objective of our results. In our results, we show the existence of topological non-trivial phases for spiral magnetic chain in the zigzag edge. With this we make a phase diagram. We also find oscillation in the energy spectrum and the topological phase changes with the oscillation, this is different from square lattice in which we should not have a change in the topological phase[2]. We conclude this work with experimental implications of our result and possible developments.

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Kane-Mele Hubbard model on a zigzag ribbon: Stability of the topological edge states and quantum phase transitions

Cited by 10 publications

References 50 publications

Exact diagonalization study for nanographene: Modulation of charge and spin, magnetic phase diagram, and thermodynamics

Exact diagonalization study for nanographene: Modulation of charge and spin, magnetic phase diagram, and thermodynamics

Quantum Monte Carlo study of strange correlator in interacting topological insulators

Impurezas magnéticas no modelo de Kanie-Mele com supercondutividade

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