基于张量网络的$(2+1)$维SU(2)晶格规范理论中的非稳定化与纠缠
Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks
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中文总结 AI 辅助
利用张量网络研究$(2+1)$维SU(2)晶格规范理论基态的非稳定化，证明非局域魔法是优于SRE的规范-物质去局域化交叉探针，并给出夹心关系的更强下界。
中文摘要 AI 辅助
我们在$(2+1)$维含物质的$\u0010mathrm{SU}(2)$哈密顿晶格规范理论中研究基态的非稳定化（魔法），该理论在硬核胶子截断下以穿衣位点基表述，并限制在零重子数扇区。利用矩阵乘积态，我们计算了魔法的三个侧面：二阶稳定子Rényi熵（SRE）$M_2$、其非局域分量$M_2^{\rm NL}$，以及基于纠缠谱反平坦度$F$的下界。我们还证明了夹心关系的更强形式：$-\u0010log_2(1-4F)\u0010le M_2^{\rm NL}\u0010le M_2$；下界依赖于我们为任意Schmidt基和秩获得的更强不等式，从而解决了寻找最大下界的开放问题。我们强调一个结构上的区别，使得非局域量成为物理上更优的诊断：完整的SRE依赖于将规范不变的局域希尔伯特空间编码为量子比特的（非唯一）方式，而非局域魔法和反平坦度在位点局域重编码下不变，因此是态和二分固有的。通过在最大$6\u0010times 6$晶格上改变规范耦合，键维数最大为128，我们发现非局域魔法相比完整SRE或规范不变的纠缠熵，提供了更尖锐且更有利于键维数的规范-物质去局域化交叉探针，在远低于收敛基态本身所需键维数下仍保留清晰信号。
英文摘要
We study non-stabilizerness (magic) in the ground state of $(2+1)$-dimensional $\mathrm{SU}(2)$ 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 $M_2^{\rm NL}$, 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: $-\log_2(1-4F)\le M_2^{\rm NL}\le M_2$; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, thus resolving the open problem of finding the maximal lower bound. 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, both the non-local magic 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 on lattices up to $6\times 6$ with bond dimension up to $128$, we find that the non-local magic 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.
发表机构
- North Carolina State University（北卡罗来纳州立大学）
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