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

García-Martínez, N.A.; Grushin, Adolfo G.; Neupert, Titus; Valenzuela, B.; Castro, Eduardo V.

doi:10.1103/physrevb.88.245123

Cited by 66 publications

(78 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These states of matter possess both conventional order, characterized by an order parameter and a broken symmetry, and protected edge states associated with a topological quantum number. Interactiondriven QAH and QSH phases were first conceived in the context of 2D honeycomb lattice Dirac fermions [10] assuming sufficiently strong electronic repulsions although more recent analytical and numerical works question the proposal for this particular model [11][12][13][14].On the contrary, it has been proposed that 2D systems with a quadratic band crossing point (QBCP) are unstable to electronic correlation because of the finite density of states at the Fermi level leading to the possibility of The relationship between fixed points QAH and QAH-II is provided in the inset figure of Fig. 2(a).…”

mentioning

confidence: 99%

Fate of interaction-driven topological insulators under disorder

et al. 2017

View full text Add to dashboard Cite

We analyze the effect of disorder on the weak-coupling instabilities of quadratic band crossing point (QBCP) in two-dimensional Fermi systems, which, in the clean limit, display interactiondriven topological insulating phases. In the framework of a renormalization group procedure, which treats fermionic interactions and disorder on the same footing, we test all possible instabilities and identify the corresponding ordered phases in the presence of disorder for both single-valley and two-valley QBCP systems. We find that disorder generally suppresses the critical temperature at which the interaction-driven topologically non-trivial order sets in. Strong disorder can also cause a topological phase transition into a topologically trivial insulating state.PACS numbers: 73.43. Nq, 71.55.Jv, 11.30.Qc The study of topological phases of matter is one of the most active research areas in contemporary condensed matter physics. The explanation of the quantum Hall effect in terms of the topological properties of the Landau levels [1,2] in the 1980's triggered an intense research effort in the theoretical prediction [3][4][5] and the experimental discovery [6,7] of a plethora of different topologically non-trivial quantum phases. In two-dimensional (2D) insulating systems only two distinct topological non-trivial phases can be realized according to the well-established classification of topological insulators and superconductors [8,9] : (i) the quantum anomalous Hall state (QAH) [3] with a time-reversal symmetry-broken ground state and topologically protected chiral edge states and (ii) the time-reversal invariant quantum spin Hall (QSH) state [4,5], which possesses helical edge states with counterpropagating electrons of opposite spins.In recent years, attention has gradually shifted from non-interacting topological states of matter towards interaction-driven topological phases:many-particle quantum ground-states in which chiral orbital currents or spin-orbit couplings are spontaneously generated by electronic correlations. These states of matter possess both conventional order, characterized by an order parameter and a broken symmetry, and protected edge states associated with a topological quantum number. Interactiondriven QAH and QSH phases were first conceived in the context of 2D honeycomb lattice Dirac fermions [10] assuming sufficiently strong electronic repulsions although more recent analytical and numerical works question the proposal for this particular model [11][12][13][14].On the contrary, it has been proposed that 2D systems with a quadratic band crossing point (QBCP) are unstable to electronic correlation because of the finite density of states at the Fermi level leading to the possibility of The relationship between fixed points QAH and QAH-II is provided in the inset figure of Fig. 2(a).weak-coupling interaction-driven topological insulating phases [15][16][17]. And, indeed, QAH and QSH phases generated by electronic repulsions occur both in the checkerboard lattice model [15,18], and in two-valley QB...

show abstract

mentioning

confidence: 99%

Fate of interaction-driven topological insulators under disorder

et al. 2017

View full text Add to dashboard Cite

show abstract

“…However, relatively large electron-electron Coulomb interactions are required to induce chiral states due to the vanishing density of electron states. [14,15].…”

Section: Introductionmentioning

confidence: 99%

Exotic magnetic orderings in the kagome Kondo-lattice model

et al. 2014

View full text Add to dashboard Cite

We consider the Kondo-lattice model on the kagome lattice and study its weak-coupling instabilities at band filling fractions for which the Fermi surface has singularities. These singularites include Dirac points, quadratic Fermi points in contact with a flat band, and Van Hove saddle points. By combining a controlled analytical approach with large-scale numerical simulations, we demonstrate that the weak-coupling instabilities of the Kondo-lattice model lead to exotic magnetic orderings. In particular, some of these magnetic orderings produce a spontaneous quantum anomalous Hall state.

show abstract

“…A major obstacle is that, instead of triggering the desired spontaneous TRS breaking, strong interactions tend to stabilize competing solid orders by breaking the translational or rotational lattice symmetry. Thus, the putative topological phase is usually preempted by various competing states [31][32][33][34][35][36]. Moreover, it is also technically challenging to detect such exotic phases with spontaneous TRS breaking, as the TRS partners usually tend to couple on finite-size systems.…”

mentioning

confidence: 99%

“…This subject has attracted vigorous research due to support from mean-field studies, followed by low-energy renormalization-group analysis [13,16], and the existence of such topological phases has been suggested for the extended Hubbard model on various lattice models [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, unbiased numerical simulations, such as exact diagonalization (ED) and density-matrix renormalization-group (DMRG) studies, found competing states other than topological phases as the true ground states in all previously proposed systems with Dirac points [31][32][33][34] or quadratic band touching points [35,36]. A major obstacle is that, instead of triggering the desired spontaneous TRS breaking, strong interactions tend to stabilize competing solid orders by breaking the translational or rotational lattice symmetry.…”

mentioning

confidence: 99%

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

et al. 2016

View full text Add to dashboard Cite

Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. Here, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry. We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Importantly, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Thus, we identify the liquid phase as a quantum Hall phase, which provides a "proof-of-principle" demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band. DOI: 10.1103/PhysRevLett.117.096402 Introduction.-Topological states of matter have led to an ongoing revolution of our fundamental understanding of quantum materials, as exemplified by the discoveries of the integer quantum Hall (IQH) effect [1,2], the quantum anomalous Hall (QAH) effect [3][4][5], and the quantum spin Hall effect [6][7][8]. Crucially, such topological phases emerge from noninteracting electronic structures with nontrivial topology, where a strong magnetic field or a large spin-orbit coupling is typically necessary. Despite great achievements, most of the materials that have exhibited unique topological properties to date can be understood based on noninteracting physics originating from nontrivial band physics. This limitation has inspired recent enthusiasm in exploring topological phases in "trivial" materials [9][10][11][12][13], without the requirement of a nontrivial invariant encoded in a single-particle wave function or band structure. Finding such novel phases can significantly enrich the class of topological materials and thus is of great importance.The strong correlation between electrons can dramatically change the noninteracting physics and induce spontaneous symmetry breakings. Therefore, many-body interaction is expected to enable topological phases in strongly correlated systems by generating circulating currents and spontaneously breaking time-reversal symmetry (TRS), which act as an effective magnetic field or spin-orbit coupling [12,14,15]. This subject has attracted vigorous research due to support from mean-field studies, followed by low-energy renormalization-group analysis [13,16], and the existence of such topological phases has been suggested for the extended Hubbard model on various lattice models [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, unbiased numerical simulations, such as

show abstract

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

Cited by 66 publications

References 35 publications

Fate of interaction-driven topological insulators under disorder

Fate of interaction-driven topological insulators under disorder

Exotic magnetic orderings in the kagome Kondo-lattice model

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

Contact Info

Product

Resources

About