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arXiv:1606.01124 · Physical review. B./Physical review. B

Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional renormalization group calculation with high-wave-vector resolution

David Sánchez de la Peña, Julian Lichtenstein, Carsten Honerkamp A

Published Feb 27, 2017• 37 citations
arXivHTMLPDF

Abstract

We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional renormalization group scheme, which allows for highly resolved calculations of wave-vector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure ${n}^{\text{th}}$ nearest-neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when nonlocal density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough nonlocal terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semimetallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second-nearest-neighbor interactions is not realized in our results with high momentum resolution.

DOI
10.1103/physrevb.95.085143

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We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional renormalization group scheme, which allows for highly resolved calculations of wave-vector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure nth{n}^{\text{th}}nth nearest-neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when nonlocal density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough nonlocal terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semimetallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second-nearest-neighbor interactions is not realized in our results with high momentum resolution.
Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group, and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physically relevant case of spin-1/2 fermions with onsite, nearest-neighbor, and second-nearest-neighbor repulsion. To this end, we employ the multipatch functional renormalization group for correlated fermions with refined momentum resolution observing the emergence of an antiferromagnetic spin-density wave and a charge-density wave for dominating onsite and nearest-neighbor repulsions, respectively. For dominating second-nearest neighbor interaction our results favor an ordering tendency towards a charge-modulated ground state over the topological Mott insulating state. The latter evades a stabilization as the leading instability by the additional onsite interaction.
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' wave vector 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{p}_{z}pz​ electrons.
We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and second-nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the second-nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fermionic systems. Our fRG results hint at a strong suppression of the scattering processes stabilizing the topological Mott insulator. From analyzing the effects of fermionic fluctuations, we obtain a phase diagram, which is the result of the competition of various charge ordering instabilities.
The Hubbard and extended Hubbard models on the honeycomb lattice can be seen as prototype models of a single-layer graphene placed in a high dielectric constant environment that screens the Coulomb interaction. Taking advantage of the absence of a sign problem at half-filling, we study this problem with clusters up to 96 sites with the determinant quantum Monte Carlo method as an impurity solver for the dynamical cluster approximation at finite temperatures. After determining the stability of the semimetallic phase to interaction-induced spin-density wave (SDW), charge-density wave (CDW), and Mott insulating phases, we study the single-particle dynamics of the Dirac fermions. We show that when spontaneous symmetry breaking is avoided, the semimetallic phase is a stable Fermi liquid in the presence of repulsive interactions and that Kondo screening dominates the low temperature regime, even though there is a $\ensuremath{\rho}(\ensuremath{\omega})=|\ensuremath{\omega}|$ type local density of states. We also investigate the impact of the correlation effects on the renormalization of the Fermi velocity vF{v}_{F}vF​. We find that vF{v}_{F}vF​ is not renormalized when only on-site repulsion UUU is present, but that near-neighbor repulsion VVV does renormalize vF{v}_{F}vF​. This may explain the variations between different measurements of vF{v}_{F}vF​ in graphene.
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with fff-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.
A simple yet paradigmatic model for the interplay of strong electronic correlations and geometric frustration is the triangular lattice Hubbard model. Recently it was proposed that moir\'e structures of transition metal dichalcogenides can be used to simulate extended versions that include nonlocal density-density interactions. We study competing instabilities of interacting electrons in such an extended Hubbard model on the triangular lattice near a filling where the density of states has a Van Hove singularity. We employ a truncated-unity functional renormalization group approach to investigate two cases: a paradigmatic minimally extended Hubbard model and a specific model with parameters that are applicable to heterobilayers of transition metal dichalcogenides. We unravel rich phase diagrams, including tendencies to spin-density-wave order and unconventional pairing, which can give rise to topological superconductivity. We classify the symmetry of the superconducting instabilities according to their irreducible representations and show that higher lattice harmonics are dominant when the nearest-neighbor interaction is sizable indicating pair formation between second-nearest neighbors. The phenomenological consequences can be enhanced spin and thermal quantum Hall responses in a topological superconductor.