临界伊辛链中Shannon-Renyi边界相的微观起源
Microscopic Origin of the Shannon Renyi Boundary Phase in the Critical Ising Chain
浏览论文内容
中文总结 AI 辅助
该研究揭示临界伊辛链的Born分布等价于弱平方反比经典伊辛模型的宇称边界，通过Cauchy核精确构造，导出$n>1$时的通用对数项，并阐明边界相的微观起源。
中文摘要 AI 辅助
Shannon-Renyi熵探测量子多体态的完整测量分布，但即使在自由费米子系统中，其微观评估仍然困难。我们证明临界横向场伊辛链的Born分布恰好是弱平方反比经典伊辛模型的宇称边界，这一结构由其概率核的Cauchy形式揭示。该构造在有限尺寸下对每个实数$n>0$都是精确的，并分离出控制$n>1$热力学的长距离扇区。切割有限区间直接由缺失的$1/r^2$相互作用生成普遍的$c\,n/[8(n-1)]$对数，其中$c=1/2$为伊辛中心荷。在环上，显式有限尺寸因子没有常数项，而任何额外的非整数奇异性被限制在仅剩的环自由能中。所有显式长距离贡献仅在$n=1$时变为边缘。
英文摘要
Shannon--Rényi entropies probe the full measurement distribution of a quantum many-body state, but their microscopic evaluation remains difficult even in free-fermion systems. We show that the Born distribution of the critical transverse-field Ising chain is exactly the parity boundary of a weak inverse-square classical Ising model, a structure revealed by the Cauchy form of its probability kernel. The construction is exact at finite size for every real $n>0$ and isolates the long-distance sectors controlling the $n>1$ thermodynamics. Cutting a finite interval generates the universal $c\,n/[8(n-1)]$ logarithm directly from the missing $1/r^2$ interactions, with $c=1/2$ the Ising central charge. On the ring, the explicit finite-size factor has no constant term, while any additional noninteger singularity is confined to a residual cycle-only free energy. All explicit long-distance contributions become marginal only at $n=1$.
发表机构
- Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
