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arXiv:2606.18973 · Physical review. B./Physical review. B

Emergence of Resonating Valence-Bond Correlations in Stretched Graphene

Sam Azadi, A. Principi, T. D. Kühne, M. S. Bahramy

cond-mat.str-elcond-mat.mes-hallcond-mat.supr-conquant-phSubmitted Jun 17, 2026• Announced Jun 18, 2026• 0 citations
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Abstract

Electronic correlations in graphene are generally considered weak due to the large bandwidth of its $π$ electrons. Here we show that tensile expansion of the honeycomb lattice provides a direct route to enhancing correlation effects. Using variational and diffusion quantum Monte Carlo, we compare a conventional Jastrow-Slater determinant wave function with a resonating-valence-bond (RVB) Jastrow-antisymmetrized geminal product ansatz for a series of stretched graphene lattices. We find that the energy gain of the RVB state relative to the single-determinant description increases with bond expansion up to a critical strain $δ_{\mathrm{cr}}$, and decreases beyond it, revealing a nonmonotonic evolution of electronic correlations. The crossover is found to occur in the range $15\% < δ_{\mathrm{cr}} < 20\%$, in agreement with mechanical stability limits. This behavior indicates a transition from a weakly correlated Dirac semimetal to a regime with enhanced non-dynamic correlation and short-range singlet pairing. Our results provide direct many-body evidence that lattice expansion drives graphene into a regime where RVB-like correlations become energetically favorable, offering a simple route to tuning correlation effects in Dirac materials.

Journal reference
Phys. Rev. B 114, L111110 (2026)
DOI
10.1103/96cl-xq62

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•Jan 1, 2011•0 citations
Electronic correlations in graphene are generally considered weak due to the large bandwidth of its πππ electrons. Here we show that tensile expansion of the honeycomb lattice provides a direct route to enhancing correlation effects. Using variational and diffusion quantum Monte Carlo, we compare a conventional Jastrow-Slater determinant wave function with a resonating-valence-bond (RVB) Jastrow-antisymmetrized geminal product ansatz for a series of stretched graphene lattices. We find that the energy gain of the RVB state relative to the single-determinant description increases with bond expansion up to a critical strain δcrδ_{\mathrm{cr}}δcr​, and decreases beyond it, revealing a nonmonotonic evolution of electronic correlations. The crossover is found to occur in the range 15%<δcr<20%15\% < δ_{\mathrm{cr}} < 20\%15%<δcr​<20%, in agreement with mechanical stability limits. This behavior indicates a transition from a weakly correlated Dirac semimetal to a regime with enhanced non-dynamic correlation and short-range singlet pairing. Our results provide direct many-body evidence that lattice expansion drives graphene into a regime where RVB-like correlations become energetically favorable, offering a simple route to tuning correlation effects in Dirac materials.
We determine the resonating-valence-bond (RVB) state in graphene using real-space quantum Monte Carlo with correlated variational wave functions. Variational and diffusion quantum Monte Carlo (DMC) calculations with Jastrow-Slater-determinant and Jastrow-antisymmetrized-geminal-power ansatze are employed to evaluate the RVB pairing energy. Using a rectangular graphene sample that lacks π/3π/3π/3 rotational symmetry, we found that the single-particle energy gap near the Fermi level depends on the system size along the xxx-direction. The gap vanishes when the length satisfies Lx=3n3dL_x=3n\sqrt{3}dLx​=3n3​d, where nnn is an integer and ddd is the carbon-carbon bond length, otherwise, the system, exhibits a finite gap. Our DMC results show no stable RVB pairing in the zero-gap case, whereas the opening of a finite gap near the Fermi level stabilizes the electron pairing. The DMC predicted absolute value of pairing energy at the thermodynamic limit for a finite-gap system is ∼0.48(1)\sim 0.48(1)∼0.48(1) mHa/atom. Our results reveal a feometry-driven electron pairing mechanism in the confined graphene nanostructure.
An extended Hubbard model on a honeycomb lattice with two orbitals per site at charge neutrality is investigated with unbiased large-scale quantum Monte Carlo simulations. The Fermi velocity of the Dirac fermions is renormalized as the cluster charge interaction increases, until a mass term emerges and a quantum phase transition from Dirac semimetal to valence bond solid (VBS) insulator is established. The quantum critical point is discovered to belong to the 3D N=4 Gross-Neveu chiral XY universality with the critical exponents obtained at high precision. Further enhancement of the interaction drives the system into two different VBS phases, the properties and transition between them are also revealed. Since the model is related to magic-angle twisted bilayer graphene, our results may have relevance towards the symmetry breaking order at the charge neutrality point of the material, and associate the wide range of universal strange metal behavior around it with quantum critical fluctuations.
We study bond and spin correlations of the nearest-neighbor resonating valence bond (RVB) wave function for a SU(2) symmetric S=1/2S=1/2S=1/2 antiferromagnet on the honeycomb lattice. We find that spin correlations in this wave function are short ranged, while the bond energy correlation function takes on an oscillatory power-law form $D(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{w}(2)}$, where $\mathbf{Q}=(2\ensuremath{\pi}/3,\ensuremath{-}2\ensuremath{\pi}/3)$ is the wave vector corresponding to ``columnar'' valence-bond solid order on the honeycomb lattice, and ${\ensuremath{\eta}}_{w}(2)\ensuremath{\approx}1.49(3)$. We use a recently introduced large-ggg expansion approach to relate bond-energy correlators of the SU(g)\mathrm{SU}(g)SU(g) wave function to dimer correlations of an interacting fully packed dimer model with a three-dimer interaction of strength $V(g)=\ensuremath{-}ln(1+1/{g}^{2})$. Putting g=2g=2g=2, we find numerically that the dimer correlation function ${D}^{d}(\stackrel{P\vec}{r})$ of this dimer model has power-law behavior ${D}^{d}(\stackrel{P\vec}{r})\ensuremath{\sim}cos(\mathbf{Q}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{r})/{|\stackrel{P\vec}{r}|}^{{\ensuremath{\eta}}_{d}(2)}$ with ${\ensuremath{\eta}}_{d}(2)\ensuremath{\approx}1.520(15)$, in rather good agreement with the wave function results. We also study the same quantities for g=3,4,10g=3,4,10g=3,4,10 and find that the bond-energy correlations in the SU(g)\mathrm{SU}(g)SU(g) wave function are consistently well reproduced by the corresponding dimer correlations in the interacting dimer model.
We perform sign-problem-free determinant quantum Monte Carlo simulations of the optical Su-Schrieffer-Heeger model on a half-filled honeycomb lattice. In particular, we investigate the model's semimetal (SM) to Kekul\'e valence bond solid (KVBS) phase transition at zero and finite temperatures as a function of phonon energy and interaction strength. Using hybrid Monte Carlo sampling methods, we can simulate the model near the adiabatic regime, allowing us to access regions of parameter space relevant to graphene. Our simulations suggest that the SM-KVBS transition is weakly first-order at all temperatures, with graphene situated close to the phase boundary in the SM region of the phase diagram. Our results highlight the important role bond-stretching phonon modes play in the formation of KVBS order in strained graphene-derived systems.
Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin-spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.
Three models of strongly correlated electron systems have been studied in this thesis: the Shastry-Sutherland quantum antiferromagnet, the quantum spin liquid emerging out of correlated Dirac fermions on the honeycomb lattice, and the edge-state magnetism in the graphene nanoribbons. The methods applied are quantum Monte Carlo simulations, namely, stochastic series expansion quantum Monte Carlo for bosonic (spin) systems and projector auxiliary field quantum Monte Carlo for fermionic systems. The stochastic series expansion quantum Monte Carlo method is applied to study the ground state properties as well as the magnetization process of the spin-1/2 easy-axis Heisenberg model on the Shastry-Sutherland lattice. The quantum phase transitions between a N\'eel state, a dimer triplet state and a ferromagnetic XY phase have been characterized by finite size scaling analysis. The crystalline structures of the triplon magnetic excitations in the magnetic plateaus have been identified. The projector auxiliary field quantum Monte Carlo is applied to explore the ground state phase diagram of the SU(2) Hubbard model on the honeycomb lattice. The interplay between the relativistic Dirac dispersion, the vanishing density of states at half-filling and the strong quantum fluctuations, drives the system from a semimetal at weak coupling to an antiferromagnetic Mott insulator in the strong coupling regime. In between these phases there emerges an unexpected quantum spin liquid with no symmetry breaking in any channel. After careful finite size scaling analysis of various correlation functions, the quantum spin liquid phase is characterized as a short-range resonating valence bond state with a finite spin gap to all magnetic excitations. The study of edge-state magnetism in graphene nanoribbons is more experimentally motivated. The projector auxiliary field quantum Monte Carlo method is used to measure the static spin-spin correlation function, the single-particle spectral function, as well as the dynamic spin structure factor along the zigzag edge of graphene nanoribbons. A dominant low energy peak generated by the Coulomb interaction in the single-particle spectral function is identified as the dynamical signature of edge-state magnetism. The magnetic excitations along the zigzag edge show a linear dispersion at low energies due to the effective antiferromagnetic coupling of the edges across the ribbon. The magnetic excitations are damped by scattering processes into the particle-hole continuum at high energies.