2024/05/01 by Yizhuang Liu, Liu, Yizhuang
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2405.00550
openalex publication_date 2024/05/01 · openalex created_date 2024/05/04 · openalex updated_date 2026/07/28
In this work, we investigate quantitative properties of correlation functions on the boundaries between two 2D Ising-like models with dual parameters β and β⋆. Spin-spin correlators in such constructions without reflection symmetry with respect to transnational-invariant directions are usually represented as 2× 2 block Toeplitz determinants which are usually significantly harder than the scalar (1× 1 block) versions. Nevertheless, we show that for the specific β/β⋆ boundaries considered in this work, the symbol matrices allow explicit commutative Wiener-Hopf factorizations. As a result, the constants E(a) and E( a) for the large n asymptotics still allow explicit representations that generalize the strong Szegö's theorem for scalar symbols. However, the Wiener-Hopf factors at different z do not commute. We will show that due to this non-commutativity, ``logarithmic divergences'' in the Wiener-Hopf factors generate certain ``anomalous terms'' in the exponential form factor expansions of the re-scaled correlators. Since our boundaries in the naive scaling limits can be formulated as certain integrable boundaries/defects in 2D massive QFTs, the results of this work facilitate detailed comparisons with bootstrap approaches.