Topological insulators and Mott physics from the Hubbard interaction

Rachel, Stephan; Hur, Karyn Le

doi:10.1103/physrevb.82.075106

Cited by 311 publications

(526 citation statements)

References 105 publications

(166 reference statements)

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“…The U(1) basis: Obviously, the U(1) symmetry operator in the U(1) basis is U U 1 (α)U −1 = e iα i S z i =Ũ 1 (α) where U = n e i π 2 σxn1 is the unitary transformation between the original basis and the U(1) basis listed above Eq. (23). TheŨ 1 (α) symmetry directly leads to Eq.…”

Section: The Original Basismentioning

confidence: 99%

“…For example, Ref. [23] studied the effects of U on Kane-Mele model [4,5] (called Kane-Mele-Hubbard model with the S z conserving SOC), focusing on the stability of topological insulator and the corresponding helical edge states against the interactions U . Ref.…”

Section: Synthetic Rotated Spin-s Heisenberg Model In the Strong mentioning

confidence: 99%

“…In Sec.II, starting from the spinor boson Hubbard model in the presence of non-Abelian gauge fields (Fig.1a), in the strong coupling limit, we derive the Rotated Ferromagnetic Heisenberg model (RFHM), also stress its crucial differences than the previously well known modes such as Heisenberg model [1,2], Kitaev model [19,20], DzyaloshinskiiMoriya (DM) interaction [21,22] and some other strong coupling models [23,24]. In Sec.III, we introduce the Wilson loops (Fig.1b) to characterize gauge equivalent classes and frustrations of the RFHM.…”

Section: Introductionmentioning

confidence: 99%

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Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

2015

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We study quantum magnetism of interacting spinor bosons at integer fillings hopping in a square lattice in the presence of of non-Abelian gauge fields. In the strong coupling limit, it leads to the Rotated ferromagnetic Heisenberg model (RFHM) which is a new class of quantum spin model. We introduce Wilson loops to characterize frustrations and gauge equivalent classes. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground state. It supports not only commensurate magnons, but also a new gapped elementary excitation: in-commensurate magnons with two gap minima continuously tuned by the SOC strength. At low temperatures, these magnons lead to dramatic effects in many physical quantities such as density of states, specific heat, magnetization, uniform susceptibility, staggered susceptibility and various spin correlation functions. The commensurate magnons lead to a pinned central peak in the angle resolved light or atom Bragg spectroscopy. However, the in-commensurate magnons split it into two located at their two gap minima. At high temperatures, the transverse spin structure factors depend on the SOC strength explicitly. The whole set of Wilson loops can be mapped out by measuring the specific heat at the corresponding orders in the high temperature expansion. We argue that one gauge may be realized in current experiments and other gauges may also be realized in near future experiments. The results achieved along the exact solvable line sets up the stage to investigate dramatic effects when tuning away from it by various means. We sketch the crucial roles to be played by these magnons at other equivalent classes, with spin anisotropic interactions and in the presence of finite magnetic fields. Various experimental detections of these new phenomena are discussed. Rotated Anti-ferromagnetic Heisenberg model are also briefly mentioned.

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Section: The Original Basismentioning

confidence: 99%

Section: Synthetic Rotated Spin-s Heisenberg Model In the Strong mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

2015

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“…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%

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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“…These proposals stimulate studies of the correlation effect in the topological phases, which is one of the current important issues. So far, the correlation effects on topological phases have been extensively studied [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] since electron correlations under such nontrivial conditions are expected to produce exotic phenomena. For example, the phase competition between topological phases and long-range ordered phases has been discussed [14][15][16][17][18][19][20][21][22][23], and nontrivial phases induced by Coulomb interactions have been proposed [24][25][26].…”

Section: Introductionmentioning

confidence: 99%