Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization

Volpez, Yanick; Scherer, Daniel D.; Scherer, Michael M.

doi:10.1103/physrevb.94.165107

Cited by 21 publications

(26 citation statements)

References 52 publications

(75 reference statements)

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“…On the other hand, when V 2 increases, we find three insulating phases characterized by different charge-and magnetic-order patterns. As we detail below, two nonmagnetic CDW phases are similar to the ones obtained from mean-field [24], fRG [25,26], ED [17][18][19], and iDMRG [20] calculations. In addition to the two phases, we find a CDW phase with antiferromagnetic order in the large-U and -V 2 region.…”

Section: A Mean-field Phase Diagramsupporting

confidence: 57%

“…Recent extensive research on the honeycomb extended Hubbard model by ED [17][18][19], iDMRG [20], auxiliaryfield quantum Monte Carlo (AFQMC) [28], variational Monte Carlo (VMC) [24], and functional renormalization group (fRG) [25,26,29] suggests that TMI is less likely than conventional ordered states, often CDW, at half filling. This fact leads us to ask the following questions: and CDW states.…”

Section: Introductionmentioning

confidence: 99%

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Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model

et al. 2018

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We investigate the competition between charge-density-wave (CDW) states and a Coulomb interaction-driven topological Mott insulator (TMI) in the honeycomb extended Hubbard model. For the spinful model with on-site (U ) and next-nearest-neighbor (V2) Coulomb interactions at half filling, we find two peculiar six-sublattice charge-density-wave insulating states by using variational Monte Carlo simulations as well as the Hartree-Fock approximation. We observe that conventional ordered states always win with respect to the TMI. The ground state is given in the large-V2 region by a CDW characterized by a 220200 (001122) charge configuration for smaller (larger) U , where 0, 1, and 2 denote essentially empty, singly occupied, and doubly occupied sites. Within the 001122-type CDW phase, we find a magnetic transition driven by an emergent coupled-dimer antiferromagnet on an effective square lattice of singly occupied sites. Possible realizations of the found states are discussed.

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Section: A Mean-field Phase Diagramsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model

et al. 2018

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“…The phase diagram of this model is still an active field of research, see, e.g., Refs. [9][10][11][13][14][15][16][17] for various refined and extended treatments. Due to the complexity of the flow equations, so far it has not been possible to implement an FRG scheme that takes the full frequency dependence, the full momentum dependence and the self-energy flow into account.…”

Section: A General Discussionmentioning

confidence: 99%

“…Numerous authors have extended and refined the treatment since then, for example in Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17]. Depending on the geometry, the interaction strength, and doping, different leading-order instabilities were identified.…”

Section: Introductionmentioning

confidence: 99%

Detecting phases in one-dimensional many-fermion systems with the functional renormalization group

Markhof¹,

Sbierski²,

Meden³

et al. 2018

Phys. Rev. B

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The functional renormalization group (FRG) has been used widely to investigate phase diagrams, in particular the one of the two-dimensional Hubbard model. So far, the study of one-dimensional models has not attracted as much attention. We use the FRG to investigate the phases of a onedimensional spinless tight-binding chain with nearest and next-nearest neighbor interactions at half filling. The phase diagram of this model has already been established with other methods, and phase transitions from a metallic phase to ordered phases take place at intermediate to strong interactions. The model is thus well suited to analyze the potential and the limitations of the FRG in this regime of interactions. We employ flow equations that are exact up to second order in the interaction, which implies that we take into account the frequency dependence of the two-particle vertex as well as the feedback of the dynamic self-energy. For intermediate nearest neighbor interactions, our scheme captures the phase transition from a metallic phase to a charge density wave with alternating occupation. The critical interaction, at which this transition occurs, is underestimated due to our approximations. Similarly, for intermediate next-nearest neighbor interactions, we observe a transition to a charge density wave with occupation pattern ..00110011... We show that taking into account a feedback of the two-particle vertex in the flow equation is essential for the detection of those phases. arXiv:1803.00272v2 [cond-mat.str-el]

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“…The interplay among these coupling terms caused some controversy regarding possible exotic ground states, hinting towards spin liquid and topologically non-trivial phases 20 , where most studies focused on the case of spinless fermions. However, in more recent studies they are falling out of favor for the more mundane charge order, both in the spinless 29 as well as in the spin-1/2 case 30,31 . As shown in Ref.…”

Section: B Crpa Parameters Without Strainmentioning

confidence: 98%

Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions

et al. 2017

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We study the quantum many-body ground states of electrons on the half-filled honeycomb lattice with short-and long-ranged density-density interactions as a model for graphene. To this end, we employ the recently developed truncated-unity functional renormalization group (TU-fRG) approach which allows for a high resolution of the interaction vertex' wavevector dependence. We connect to previous lattice quantum Monte Carlo (QMC) results which predict a stabilization of the semimetallic phase for realistic ab initio interaction parameters and confirm that the application of a finite biaxial strain can induce a quantum phase transition towards an ordered ground state. In contrast to lattice QMC simulations, the TU-fRG is not limited in the choice of tight-binding and interaction parameters to avoid the occurrence of a sign problem. Therefore, we also investigate a range of parameters relevant to the realistic graphene material which are not accessible by numerically exact methods. Although a plethora of charge density waves arises under medium-range interactions, we find the antiferromagnetic spin-density wave to be the prevailing instability for long-range interactions. We further explore the impact of an extended tight-binding Hamiltonian with second-nearest neighbor hopping and a finite chemical potential for a more accurate description of the band structure of graphene's pz electrons.

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Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization

Cited by 21 publications

References 52 publications

Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model

Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model

Detecting phases in one-dimensional many-fermion systems with the functional renormalization group

Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions

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