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arXiv:2504.04800 · Journal of Physics Condensed Matter

Spin bond order driven by extended repulsive interactions in doped graphene

Jin-Song Ri, O Song-Jin, O Chol-Su

Published Aug 29, 2025• 0 citations
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Abstract

We use the truncated-unity functional renormalization group (TUFRG) to study many-body instabilities of correlated electrons in graphene doped near the van Hove singularity (VHS). The system is described by an extended Hubbard model including several Coulomb repulsions between neighboring sites. With the repulsion parameters, which turn out to be suitable for low-energy consideration of graphene, we find a spin-bond-order phase in the vicinity of the VHS. This phase gives way to a spin-density-wave phase when involving a weak additional screening. The ground-state phase diagram is presented in the space of the doping level and the screening parameter. We describe in detail both of these spin-ordered states by using recently developed TUFRG + mean-field (MF) scheme, i.e. a combined approach of TUFRG and MF theory. The collinear states are energetically preferable in both cases of the spin bond order and the spin-density wave. But if the third-nearest-neighbor hopping is absent, these spin orders become chiral. The band structures of two collinear spin-ordered states are presented, revealing the metallic behavior of the system.

DOI
10.1088/1361-648x/ae010e

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We use the truncated-unity functional renormalization group (TUFRG) to study many-body instabilities of correlated electrons in graphene doped near the van Hove singularity (VHS). The system is described by an extended Hubbard model including several Coulomb repulsions between neighboring sites. With the repulsion parameters, which turn out to be suitable for low-energy consideration of graphene, we find a spin-bond-order phase in the vicinity of the VHS. This phase gives way to a spin-density-wave phase when involving a weak additional screening. The ground-state phase diagram is presented in the space of the doping level and the screening parameter. We describe in detail both of these spin-ordered states by using recently developed TUFRG + mean-field (MF) scheme, i.e. a combined approach of TUFRG and MF theory. The collinear states are energetically preferable in both cases of the spin bond order and the spin-density wave. But if the third-nearest-neighbor hopping is absent, these spin orders become chiral. The band structures of two collinear spin-ordered states are presented, revealing the metallic behavior of the system.
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.
Controlling the ordered phases of correlated electron systems remains a central challenge in quantum materials design. Divergences in the electronic density of states, known as Van Hove singularities (VHSs), are one obvious route to such control. It is clear from recent work that the exact functional form of these divergences can profoundly affect which phases are realized; a full picture, however, remains elusive. In this work, we use both the hot-spot parquet renormalization group and the truncated-unity functional renormalization group to theoretically study the emergent correlated states of a two-dimensional square-lattice Hubbard model with VHSs at or near the Fermi level. By varying a single hopping parameter, t3t_3t3​, we are able to change the strength of the VHS divergence in the density of states from logarithmic (for t3<t3ct_3 < t_{3c}t3​<t3c​) to power-law (for t3=t3ct_3 = t_{3c}t3​=t3c​). Further increase of t3t_3t3​ (t3>t3ct_3 > t_{3c}t3​>t3c​) causes each original Van Hove point to split into two, both of the conventional logarithmic type. We show that which of these regimes we are in strongly influences the predicted ordered states. We also study the dependence on doping, and find that the ferromagnetic state that occurs at Van Hove filling in these models is unstable to very small shifts in the Fermi level, often giving way to distinct ordered states depending on whether the model is electron- or hole-doped. These results highlight the importance of tuning VHS properties to control ordered states in correlated materials, and offer design rules to engineer these phases in novel systems.
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 magnetic instabilities of the nondegenerate (s(s(s-band) and a degenerate (d(d(d-band) Hubbard model in two dimensions using many-body effects due to particle-particle diagrams and Hund's rule local correlations. The density of states and the position of the Van Hove singularity change depending on the value of next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. The Stoner parameter is strongly reduced in the sss-band case, and ferromagnetism survives only if the electron density is small and the band has flat regions. Due to next-nearest-neighbor hopping there are flat regions in $\ensuremath{\Gamma}\ensuremath{-}X$ and $\ensuremath{\Gamma}\ensuremath{-}Y$ directions. In contrast, for the ddd-band case the reduction of the Stoner parameter which follows from particle-particle correlations is much smaller and ferromagnetism survives to a large extent. Inclusion of local spin-spin correlations has a limited destabilizing effect on the magnetic states.
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.
The phase diagram of the two-dimensional extended one-band $U\ensuremath{-}V\ensuremath{-}J$ Hubbard model is considered within a mean-field approximation and two- and many-patch renormalization-group (RG) approaches near the Van Hove band fillings. At small ${t}^{\ensuremath{'}}$ and J>0,J>0,J>0, mean-field and many-patch RG approaches give similar results for the leading spin-density-wave (SDW) instability, while the two-patch RG approach that predicts a wide region of charge-flux (CF) phase becomes unreliable due to nesting effect. There is a complex competition between SDW, CF phases, and d-wave superconductivity at small ${t}^{\ensuremath{'}}$ in two- and many-patch RG approaches. The spin-flux phase, which is not stable at the mean-field level, is identified as a possible ground state at J<0J<0J<0 in both RG approaches. With increasing ${t}^{\ensuremath{'}}$ the results of all three approaches merge: d-wave superconductivity at J>0J>0J>0 and ferromagnetism at J<0J<0J<0 become the leading instabilities. For large enough V, the charge-density-wave state occurs.