Non-stabilizerness and entanglement in (2+1)-dimensional SU(2) lattice gauge theory using tensor networks
Abstract
We study non-stabilizerness (magic) in the ground state of (2+1)-dimensional SU(2) Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) M2, its non-local component M2NL, estimated by the SRE M2(ψ̃) of the computational-basis Schmidt representative ψ̃, and a lower bound in terms of the anti-flatness F of the entanglement spectrum. We also prove a stronger form of the sandwich relation: −log2(1−4F)≤ M2NL≤ M2; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, with an optimal constant. Combined with recent results, this yields the unconditional bracket max{−log2(1−4F), M2(ψ̃)−4}≤ M2NL≤ M2(ψ̃). We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, the non-local magic, its estimate M2(ψ̃), and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling for two values of the fermion mass on lattices up to 8× 8 (∼ 288 qubits) with bond dimension up to $128$, we find that the non-local magic, as estimated by M2(ψ̃), furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself.
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BibTeX
@misc{jha2026nonstabilizerness,
title = {{Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks}},
author = {Raghav G. Jha and Jaber I. Taher and Muhammad Asaduzzaman and Goksu C. Toga and Bojko N. Bakalov and Alexander F. Kemper},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.28634},
eprint = {2609.28634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28634},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-stabilizerness and entanglement in (2+1)-dimensional SU(2) lattice gauge theory using tensor networks
AU - Raghav G. Jha
AU - Jaber I. Taher
AU - Muhammad Asaduzzaman
AU - Goksu C. Toga
AU - Bojko N. Bakalov
AU - Alexander F. Kemper
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2609.28634
UR - https://arxiv.org/abs/2609.28634
AB - We study non-stabilizerness (magic) in the ground state of (2+1)-dimensional SU(2) Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) M_2, its non-local component M_2^NL, estimated by the SRE M_2(ψ̃) of the computational-basis Schmidt representative ψ̃, and a lower bound in terms of the anti-flatness F of the entanglement spectrum. We also prove a stronger form of the sandwich relation: −log_2(1−4F)≤ M_2^NL≤ M_2; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, with an optimal constant. Combined with recent results, this yields the unconditional bracket max{−log_2(1−4F), M_2(ψ̃)−4}≤ M_2^NL≤ M_2(ψ̃). We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, the non-local magic, its estimate M_2(ψ̃), and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling for two values of the fermion mass on lattices up to 8× 8 (∼ 288 qubits) with bond dimension up to $128$, we find that the non-local magic, as estimated by M_2(ψ̃), furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself.
ER -