Non-Perturbative Effects in Two-Dimensional Spin Systems.

Hole spin qubits provide one of the leading platforms for spin-based quantum computing due to their large intrinsic spin-orbit interaction (SOI), which enables fast electrical manipulation. The SOI of planar quantum dots has mostly been investigated in theoretical studies by examining the SOI already present in the two-dimensional hole gas (2DHG). Here, we study the SOI created by the in-plane confinement by deriving non-perturbative effective Hamiltonians numerically for hole spin qubits. We find that the quantum geometry of the 2DHG naturally emerges, leading to a meaningful non-perturbative definition of pseudospin valid far away from the $Γ$ -point. The SOI of the 2DHG and of the in-plane confinement have different forms; therefore, they cannot be turned off simultaneously, ruining the perfect spin-orbit switch functionality of spin qubits. We construct effective Hamiltonians using the symmetry approach for various low-dimensional hole systems: (i) a heavy-hole confined in a SiGe/Ge/SiGe heterostructure, (ii) a light-hole confined in SnGe/Ge, (iii) a gate-defined nanowire in SiGe/Ge/SiGe, and (iv) a hole confined in a Ge/Si core/shell nanowire. The non-perturbative effective Hamiltonians provide results with excellent agreement with the full Hamiltonians.Hole spin qubits provide one of the leading platforms for spin-based quantum computing due to their large intrinsic spin-orbit interaction (SOI), which enables fast electrical manipulation. The SOI of planar quantum dots has mostly been investigated in theoretical studies by examining the SOI already present in the two-dimensional hole gas (2DHG). Here, we study the SOI created by the in-plane confinement by deriving non-perturbative effective Hamiltonians numerically for hole spin qubits. We find that the quantum geometry of the 2DHG naturally emerges, leading to a meaningful non-perturbative definition of pseudospin valid far away from the $Γ$-point. The SOI of the 2DHG and of the in-plane confinement have different forms; therefore, they cannot be turned off simultaneously, ruining the perfect spin-orbit switch functionality of spin qubits. We construct effective Hamiltonians using the symmetry approach for various low-dimensional hole systems: (i) a heavy-hole confined in a SiGe/Ge/SiGe heterostructure, (ii) a light-hole confined in SnGe/Ge, (iii) a gate-defined nanowire in SiGe/Ge/SiGe, and (iv) a hole confined in a Ge/Si core/shell nanowire. The non-perturbative effective Hamiltonians provide results with excellent agreement with the full Hamiltonians.

cond-mat.mes-hallCross-listedarXiv:2606.14683Jun 15, 2026

Overlap locking and non-perturbative effects in spin glasses

Silvio Franz, Giorgio Parisi A, Federico Ricci‐Tersenghi

We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when $1 \ll ΔH \ll N$ , being $ΔH$ the coupling Hamiltonian and $N$ the size of the system. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections and to the correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model.We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when $1 \ll ΔH \ll N$, being $ΔH$ the coupling Hamiltonian and $N$ the size of the system. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections and to the correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model.

arXiv:2602.18399Feb 20, 20260 citations

Dynamics of Two-Dimensional Quantum Spin Systems

M. S. Makivić, Mark Jarrell

Springer proceedings in physicsJan 1, 19930 citations

Numerical Studies of Two-Dimensional Quantum Spin Systems

Eric S. Swanson

Jan 1, 19900 citations

Γ

-point. The SOI of the 2DHG and of the in-plane confinement have different forms; therefore, they cannot be turned off simultaneously, ruining the perfect spin-orbit switch functionality of spin qubits. We construct effective Hamiltonians using the symmetry approach for various low-dimensional hole systems: (i) a heavy-hole confined in a SiGe/Ge/SiGe heterostructure, (ii) a light-hole confined in SnGe/Ge, (iii) a gate-defined nanowire in SiGe/Ge/SiGe, and (iv) a hole confined in a Ge/Si core/shell nanowire. The non-perturbative effective Hamiltonians provide results with excellent agreement with the full Hamiltonians.

1 \ll ΔH \ll N

, being

ΔH

the coupling Hamiltonian and

N

the size of the system. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections and to the correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model.