© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2511.06506 · Physical review. B./Physical review. B

Resonating valence bond pairing energy in graphene by quantum Monte Carlo

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

cond-mat.str-elcond-mat.supr-conphysics.comp-phquant-phSubmitted Nov 9, 2025• Announced Nov 11, 2025• 1 citation

Abstract

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 $π/3$ rotational symmetry, we found that the single-particle energy gap near the Fermi level depends on the system size along the $x$-direction. The gap vanishes when the length satisfies $L_x=3n\sqrt{3}d$, where $n$ is an integer and $d$ 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 $\sim 0.48(1)$ mHa/atom. Our results reveal a feometry-driven electron pairing mechanism in the confined graphene nanostructure.

Journal reference: Phys. Rev. B 113, L121101 (2026)
DOI: 10.1103/hmmc-nhdl

Related papers

Emergence of Resonating Valence-Bond Correlations in Stretched Graphene

Sam Azadi, A. Principi, T. D. Kühne +1 more

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.

cond-mat.str-elCross-listedarXiv:2606.18973•Physical review. B./Physical review. B•Jun 18, 2026•0 citations

Twisted graphene superlattices: resonating valence bond states and magnetic properties

Florentino Lopéz‐Urías, Alberto Rubio-Ponce, Emilio Muñoz‐Sandoval +1 more

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.

Journal of Physics Condensed Matter•Jun 28, 2024•2 citations

Frustrated RVB states in 2D: classifications and short-range correlations

Fan Yang, Hong Yao

Resonating valence bond (RVB) states are of crucial importance in our intuitive understanding of quantum spin liquids in 2D. We systematically classify short-range bosonic RVB states into symmetric or nematic spin liquids by examining their flux patterns. We further map short-range bosonic RVB states into projected BCS wave functions, on which we perform large-scale Monte Carlo simulations without the minus sign problem. Our results clearly show that both spin and dimer correlations decay exponentially in all the short-range frustrated (non-bipartite or $Z_2$) bosonic RVB states we studied, indicating that they are gapped $Z_2$ quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.

arXiv:1204.6381•Apr 28, 2012•1 citation

Frustrated Resonating Valence Bond States in Two Dimensions: Classification and Short-Range Correlations

Fan Yang, Hong Yao

Resonating valence bond (RVB) states are of crucial importance in our intuitive understanding of quantum spin liquids in 2D. We systematically classify short-range bosonic RVB states into symmetric or nematic spin liquids by examining their flux patterns. We further map short-range bosonic RVB states into projected BCS wave functions, on which we perform large-scale Monte Carlo simulations without the minus sign problem. Our results clearly show that both spin and dimer correlations decay exponentially in all the short-range frustrated (nonbipartite or Z2) bosonic RVB states we studied, indicating that they are gapped Z2 quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.

Physical Review Letters•Oct 5, 2012•47 citations

A quantum spin‐liquid in correlated relativistic electrons

Ziyang Meng, Thomas C. Lang, Stefan Weßel +2 more

Abstract In recent years, an increasing number of systems displaying exotic quantum states like unconventional superconductivity, quantum spin‐liquids, or topological states were experimentally found. Here we summarize findings in quantum Monte Carlo simulations of correlated electrons on a honeycomb lattice, the structure of graphene, that revealed an unexpected spin‐liquid emerging between a state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. Moreover, we found that this quantum‐disordered state is a resonating valence‐bond (RVB) liquid, akin to the one proposed for high temperature superconductors. This was the first unbiased determination of a RVB‐liquid in an electronic system.

Annalen der Physik•Feb 6, 2012•1 citation

Stability of resonating-valence-bond state in the Hubbard model near half filling

Masahiro Miyazaki, Jun-ichiro Inoue, Sadamichi Maekawa

We have calculated the energy of the resonating-valence-bond (RVB) state made of nearest-neighbor singlet pairs in the two-dimensional Hubbard model at half filling and the energy of holes in the RVB state near half filling. The energy of the RVB state was obtained by extrapolating the result in a 6\ifmmode\times\else\texttimes\fi{}6 square lattice with the periodic boundary condition to the infinite lattice. The energy of holes was obtained by examining the first five moments of the density of states of holes in the RVB state. We find that the holes are more stabilized in the RVB state than in the N\'eel state for J/t\ensuremath{\gtrsim}0.1, where J and t are the exchange interaction and the nearest-neighbor hopping integral, respectively. We discuss the possibility of the RVB state in the high-${T}_{c}$ Cu oxides.

Physical review. B, Condensed matter•Oct 1, 1989•6 citations

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/3

rotational symmetry, we found that the single-particle energy gap near the Fermi level depends on the system size along the

x

-direction. The gap vanishes when the length satisfies

L_x=3n\sqrt{3}d

, where

n

is an integer and

d

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

\sim 0.48(1)

mHa/atom. Our results reveal a feometry-driven electron pairing mechanism in the confined graphene nanostructure.

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.

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.

Resonating valence bond (RVB) states are of crucial importance in our intuitive understanding of quantum spin liquids in 2D. We systematically classify short-range bosonic RVB states into symmetric or nematic spin liquids by examining their flux patterns. We further map short-range bosonic RVB states into projected BCS wave functions, on which we perform large-scale Monte Carlo simulations without the minus sign problem. Our results clearly show that both spin and dimer correlations decay exponentially in all the short-range frustrated (non-bipartite or

Z_2

) bosonic RVB states we studied, indicating that they are gapped

Z_2

quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.

Resonating valence bond (RVB) states are of crucial importance in our intuitive understanding of quantum spin liquids in 2D. We systematically classify short-range bosonic RVB states into symmetric or nematic spin liquids by examining their flux patterns. We further map short-range bosonic RVB states into projected BCS wave functions, on which we perform large-scale Monte Carlo simulations without the minus sign problem. Our results clearly show that both spin and dimer correlations decay exponentially in all the short-range frustrated (nonbipartite or Z2) bosonic RVB states we studied, indicating that they are gapped Z2 quantum spin liquids. Generically, we conjecture that all short-range frustrated bosonic RVB states in 2D have only short-range correlations.

Abstract In recent years, an increasing number of systems displaying exotic quantum states like unconventional superconductivity, quantum spin‐liquids, or topological states were experimentally found. Here we summarize findings in quantum Monte Carlo simulations of correlated electrons on a honeycomb lattice, the structure of graphene, that revealed an unexpected spin‐liquid emerging between a state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. Moreover, we found that this quantum‐disordered state is a resonating valence‐bond (RVB) liquid, akin to the one proposed for high temperature superconductors. This was the first unbiased determination of a RVB‐liquid in an electronic system.

We have calculated the energy of the resonating-valence-bond (RVB) state made of nearest-neighbor singlet pairs in the two-dimensional Hubbard model at half filling and the energy of holes in the RVB state near half filling. The energy of the RVB state was obtained by extrapolating the result in a 6\ifmmode\times\else\texttimes\fi{}6 square lattice with the periodic boundary condition to the infinite lattice. The energy of holes was obtained by examining the first five moments of the density of states of holes in the RVB state. We find that the holes are more stabilized in the RVB state than in the N\'eel state for J/t\ensuremath{\gtrsim}0.1, where J and t are the exchange interaction and the nearest-neighbor hopping integral, respectively. We discuss the possibility of the RVB state in the high-

{T}_{c}

Cu oxides.