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arXiv · 2511.06506

Resonating valence bond pairing energy in graphene by quantum Monte Carlo

S. Azadi·A. Principi·T. D. Kühne·M. S. Bahramy
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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 $\pi/3$ 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.

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S. Azadi, A. Principi, T. D. Kühne, M. S. Bahramy. 2025-11-09. Resonating valence bond pairing energy in graphene by quantum Monte Carlo. https://doi.org/10.1103/hmmc-nhdl

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