Phases of correlated spinless fermions on the honeycomb lattice

Daghofer, Maria; Hohenadler, Martin

doi:10.1103/physrevb.89.035103

Cited by 85 publications

(119 citation statements)

References 59 publications

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“…Despite the fact that we have not found evidence for the Chern insulator (CI) phase, it is still possible that it is realizable in the thermodynamic limit. Different approaches such as cluster mean field 31 can also prove useful to ascertain the presence of the CI phase. We hope that the conclusions of this work will motivate further explorations of the extended Hubbard model on the honeycomb lattice.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

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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“…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.…”

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confidence: 99%

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

et al. 2016

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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

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“…In particular, one does not want to rely on a purely interaction-driven spin-orbit coupling to generate the Chern insulator phase. 50 The magnetic order that appears above a critical value of U is another important feature of our results. The configurations of local moments under the CDMFT calculations are non-collinear in both bilayer and trilayer systems and they highly resemble their counterparts in the bulk material with the same tight-binding parameters, though they are different in detail because of the lowered symmetry of the films.…”

Section: Discussionmentioning

confidence: 72%

“…For Chern insulators induced "purely" by electron-electron interactions (that is, the underlying Hamiltonian has no intrinsic spin-orbit coupling at the non-interacting level), it appears that temporal fluctuations can indeed destroy the topological phase. 50 In our model-that does include a finite spinorbit coupling at the non-interacting level-we reach the opposite conclusion: Temporal fluctuations do not generally destroy an interaction-driven topological phase in two-dimensions.…”

Section: Introductionmentioning

confidence: 77%

Correlation effects in pyrochlore iridate thin films grown along the [111] direction

Chen

Hung

et al. 2015

Phys. Rev. B

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Over the past few years bulk pyrochlore iridates of the form A2Ir2O7 (where A is a rare earth element, Ir is iridium, and O is oxygen) have been studied as model systems for investigating the interplay of electronic correlations and strong spin-orbit coupling, particularly with the aim of finding correlation-driven topological phases. In this work, we use cellular dynamical mean field theory (CDMFT) to study effects of electronic correlations beyond Hartree-Fock theory in thin films of pyrochlore irradiates grown along the [111] direction. We focus on the bilayer and trilayer systems, and compute the phase diagrams of these systems as a function of electron-electron interaction strength, which is modeled by an on-site Hubbard interaction. By evaluating the Z2 invariant and Chern number using formulas based on the single-particle Green's function and the quasiparticle effective Hamiltonian, we show that on-site correlations can drive an interaction-induced topological phase transition, turning a time-reversal invariant topological insulator and a nearly flat band metal to a correlated Chern insulator (CI) in bilayer and trilayer systems, respectively. By comparing with the Hartree-Fock results, the CDMFT results show that quantum fluctuations enhance the robustness of the interaction-driven CI phase in the thin films. Furthermore, our numerical analysis of the quasiparticle spectrum reveals that the topological phases we find in our many-body calculations are adiabatically connected to those in the single-particle picture.

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Phases of correlated spinless fermions on the honeycomb lattice

Cited by 85 publications

References 59 publications

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

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

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

Correlation effects in pyrochlore iridate thin films grown along the [111] direction

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