Correlated States in Quantum Dot Clusters Coupled to a Common Superconductor
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.
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BibTeX
@misc{zonda2026correlated,
title = {{Correlated States in Quantum Dot Clusters Coupled to a Common Superconductor}},
author = {Martin Žonda and Jakub Rękas and Tobiáš Poláček and Jana Kodrlová and Vladislav Pokorný and Martin Friák},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.04608},
eprint = {2606.04608},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.04608},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Correlated States in Quantum Dot Clusters Coupled to a Common Superconductor
AU - Martin Žonda
AU - Jakub Rękas
AU - Tobiáš Poláček
AU - Jana Kodrlová
AU - Vladislav Pokorný
AU - Martin Friák
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2606.04608
UR - https://arxiv.org/abs/2606.04608
AB - 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.
ER -