Interplay of interactions, disorder, and topology in the Haldane-Hubbard model

Yi, Tian-Cheng; Hu, Sheng; Castro, Eduardo V.; Mondaini, Rubem

doi:10.1103/physrevb.104.195117

Cited by 19 publications

(5 citation statements)

References 76 publications

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“…In recent years, the TAIs and their generalizations have been revealed in various systems [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], even in some non-Hermitian systems [31][32][33][34][35][36][37] and in the presence of inter-particle interactions [38][39][40]. Some of them have been experimentally observed in engineered lattices, such as cold atomic gases [41], photonic and sonic crystals [42][43][44], electric circuits [45], and photonic quantum walks [36].…”

Section: Introductionmentioning

confidence: 99%

Topological Anderson insulators with different bulk states in quasiperiodic chains

Tang,

Liu,

Zhang

et al. 2022

Preprint

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We investigate the topology and localization of one-dimensional Hermitian and non-Hermitian Su-Schrieffer-Heeger chains with quasiperiodic hopping modulations. In the Hermitian case, phase diagrams are obtained by numerically and analytically calculating various topological and localization characters. We show the presence of topological extended, intermediate, and localized phases due to the coexistence of topological and localization phase transitions driven by the quasiperiodic disorder. In particular, we uncover three types of disorder-induced topological Anderson insulators (TAIs) with extended, intermediate, and localized bulk states in this chiral chain. Moreover, we study the non-Hermitian effects on the TAIs by considering two kinds of non-Hermiticities from the non-conjugate complex hopping phase and asymmetric hopping strength, respectively. We demonstrate that three types of TAIs preserve under the non-Hermitian perturbations with some unique localization and topological properties, such as the non-Hermitian real-complex and localization transitions and their topological nature.

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Section: Introductionmentioning

confidence: 99%

Topological Anderson insulators with different bulk states in quasiperiodic chains

Tang,

Liu,

Zhang

et al. 2022

Preprint

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“…Therefore it is of hight interest to study the effect of the local Hubbard interaction on the topological properties of the system. In particular, the following aspects have been studied: the time reversal invariant Hofstadter-Hubbard model [35][36][37][38][39] , the Haldane-Hubbard model [40][41][42][43] , the Kane-Mele-Hubbard model [44][45][46][47] , the interacting Rice-Mele model 48 , the Bernevig-Hughes-Zhang Hubbard model 49,50 , Weyl-Hubbard model 51 , SU(3) systems with artificial gauge fields 52,53 , and the Kondo lattice model [54][55][56] .…”

Section: Introductionmentioning

confidence: 99%

Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling

Titvinidze,

Legendre,

Hur

et al. 2022

Preprint

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We study the Hubbard model with time-reversal invariant flux and spin-orbit coupling and position-dependent onsite energies on the kagome lattice, using numerical and analytical methods. In particular, we perform calculations using real space dynamical mean-field theory (R-DMFT). To study the topological properties of the system, we use the topological Hamiltonian approach. We obtain a rich phase diagram: for weak and intermediate interactions, depending on the model parameters, the system is in the band insulator, topological insulator, or metallic phase, while for strong interactions the system is in the Mott insulator phase. We also investigate the magnetic phases that occur in this system. For this purpose, in addition to R-DMFT, we also use two analytical methods: perturbation theory for large interactions and onsite energies, and stochastic mean-field theory.

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“…In particular, in the strong coupling regime obtained when the interaction scale U is much stronger than the bandwidth W of a Chern band that is separated from other bands by an energy gap ∆ such that ∆ U W , electronic correlations can stabilize rich fractionalized phases [16][17][18][19]. Furthermore, correlated phases of the repulsive Haldane-Hubbard model at commensurate 1/2 and 1/4 fillings have been investigated using numerical methods and mean-field studies [20][21][22][23][24][25][26][27][28].…”

mentioning

confidence: 99%

“…In this Letter, we unveil a new scheme to investi-gate correlation effects in Chern bands, focusing on the Haldane-Hubbard model as a paradigmatic system to address the confluence of band topology and electronic correlations. Departing from previous studies [20][21][22][23][24][25][26][27][28], we analyze a new regime characterized by incommensurate fillings reached when the Fermi energy lies near VHS in the Haldane Chern bands. The diverging density of states (DOS) near localized pockets in the BZ allows a treatment of interactions at weak coupling regime using unbiased RG methods.…”

mentioning

confidence: 99%

Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

Castro¹,

Shaffer²,

Wu³

et al. 2023

Preprint

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While advances in electronic band theory have brought to light new topological systems, understanding the interplay of band topology and electronic interactions remains a frontier question. In this work, we predict new interacting electronic orders emerging near higher-order Van Hove singularities present in the Chern bands of the Haldane model. We classify the nature of such singularities and employ unbiased renormalization group methods that unveil a complex landscape of electronic orders, which include ferromagnetism, density-waves and superconductivity. Importantly, we show that repulsive interactions can stabilize long-sought pair-density-wave state and an exotic Chern supermetal, which is a new class of non-Fermi liquid with anomalous quantum Hall response. This framework opens a new path to explore unconventional electronic phases in two-dimensional chiral bands through the interplay of band topology and higher-order Van Hove singularities.

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Interplay of interactions, disorder, and topology in the Haldane-Hubbard model

Cited by 19 publications

References 76 publications

Topological Anderson insulators with different bulk states in quasiperiodic chains

Topological Anderson insulators with different bulk states in quasiperiodic chains

Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling

Emergence of Chern Supermetal and Pair-Density Wave through Higher-Order Van Hove Singularities in the Haldane-Hubbard Model

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