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arXiv:2606.04608

Correlated States in Quantum Dot Clusters Coupled to a Common Superconductor

Martin Žonda, Jakub Rękas, Tobiáš Poláček, Jana KODRLOVÁ, Vladislav Pokorný, Martin Friák

Published Jun 3, 2026• 0 citations
arXivHTMLPDF

Abstract

We study an effective model of regular quantum dot clusters coupled to a common superconductor. By applying a canonical transformation, we map the system onto a particle-number-conserving representation, enabling an efficient treatment with standard fermionic neural-network quantum-state variational Monte Carlo methods. We show that the excitation gap can close under a particular high-symmetry condition, which, in finite non-interacting systems, corresponds to crossings between singlet ground states of different character. At this high-symmetry condition the model can be mapped to a standard Hubbard model in grand-canonical ensemble with fixed chemical potential away from half-filling. Combining exact methods, density matrix renormalization group, and neural quantum-state variational Monte Carlo calculations, we identify three distinct interacting regimes: a trivial superconducting singlet phase, a strongly correlated regime related to an effective Heisenberg model, and a critical intermediate regime with qualitatively different behavior in one and two dimensions. In one-dimensional systems, the intermediate regime exhibits a sequence of singlet-doublet transitions and becomes gapless in the thermodynamic limit even for finite Coulomb interaction. In two-dimensional clusters, we find robust triplet ground states. These results connect the physics of superconducting nanostructures with correlated lattice models and show that standard fermionic neural quantum states can capture the relevant interacting regimes.

DOI
10.48550/arxiv.2606.04608

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