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arXiv:2601.13108

Superconductivity in doped symmetric mass generation insulator: a quantum Monte-Carlo study

Sibo Guo, Wei-Xuan Chang, Yi-Zhuang You, Zixiang Li

Published Jan 19, 2026• 0 citations
arXivHTMLPDF

Abstract

Understanding unconventional superconductivity (SC) driven by strong electronic correlations is a central challenge in condensed matter physics. In this work, we employ sign-problem-free quantum Monte Carlo (QMC) simulations to systematically investigate a bilayer fermionic model featuring strong interlayer antiferromagnetic (AFM) exchange and on-site repulsive Hubbard interactions. This system serves as a prototypical model for realizing a symmetric mass generation (SMG) insulator. Our numerically exact results unambiguously demonstrate that robust superconducting pairing emerges upon doping the SMG phase. Remarkably, we find that the SC order is significantly enhanced by the repulsive Hubbard interaction. Given its potential relevance to the essential features of the high-$T_c$ superconductor $\mathrm{La}_{3}\mathrm{Ni}_{2}\mathrm{O}_{7}$ under pressure, our study establishes a new paradigm for superconductivity arising from a doped SMG parent state and provides key theoretical guidance for future experimental investigations.

DOI
10.48550/arxiv.2601.13108

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How superconductivity emerges in the vicinity of an antiferromagnetic insulating state is a long-standing issue of strong correlation physics. We study the transition from an antiferromagnetic insulator to a superconductor by hole doping based on a bilayer generalization of a Hubbard model. The projector quantum Monte Carlo simulations are employed, which are sign problem free both at and away from half filling. An anisotropic Ising antiferromagnetic Mott insulating phase occurs at half filling, which is weakened by hole doping. Below a critical doping value, antiferromagnetism coexists with the singlet superconductivity, which is a pairing across each rung with an extended sss-wave symmetry. As doping further increases, the antiferromagnetic order vanishes, leaving only a superconducting phase. These results provide important information on how superconductivity appears upon doping the parent Mott-insulating state.
The competition between antiferromagnetism and superconductivity is one of the central questions in research involving strongly correlated systems. In this paper, we utilize a double-layer model containing Hubbard interaction and interlayer Heisenberg interaction to reveal their competition. This model is free of the sign problem under certain conditions, and we perform projector quantum Monte Carlo simulations to extract the ground-state correlations of magnetism and superconductivity. Our results show that the superconductivity emerges when the antiferromagnetism is suppressed by tuning the filling or the anisotropy of the interlayer Heisenberg interaction. This model can be seen as an analog of unconventional superconductors and may help us to understand the transition from an antiferromagnetic insulator to a superconductor.
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To understand correlated insulating and unconventional superconducting states in twisted bilayer graphene, we perform a systematic study of spin and pairing correlations in an effective two-orbital Hubbard model, by using the ground-state constrained-path quantum Monte Carlo method. Our numerical simulations reveal that when only the on-site Hubbard UUU is considered, the long-range magnetic order develops for $U\ensuremath{\ge}3.2t$ at half filling. Upon doping away from half filling, an analysis based on the pairing correlations and corresponding vertex contributions identifies that pairing with the d+idd+idd+id symmetry is the dominant pairing channel. As the on-site Coulomb interaction is increased, both spin correlation and effective pairing interaction are enhanced simultaneously, indicating the intimate relation between magnetism and superconductivity. An inclusion of nearest neighbor Coulomb interaction VVV results in a suppression of the d+idd+idd+id superconductivity, but it can survive in the small VVV regime. Our findings are useful for clarifying the ongoing controversy on the superconducting pairing symmetry in twisted bilayer graphene.
High-temperature superconductivity emerges in many different quantum materials, often in regions of the phase diagram where the electronic kinetic energy is comparable to the electron-electron repulsion. Describing such intermediate-coupling regimes has proven challenging as standard perturbative approaches are inapplicable. Here, we employ quantum Monte Carlo methods to solve a multiband Hubbard model that does not suffer from the sign problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free studies, we treat magnetic, superconducting, and charge degrees of freedom on an equal footing. We find an antiferromagnetic dome accompanied by a metal-to-insulator crossover line in the intermediate-coupling regime, with a smaller superconducting dome appearing in the metallic region. Across the antiferromagnetic dome, the magnetic fluctuations change from overdamped in the metallic region to propagating in the insulating region. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.