小波MER A中有限BCH纠缠子的伊辛临界性的代数障碍
An Algebraic Obstruction to Ising Criticality for Finite-BCH Entanglers in Wavelet MERA
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中文总结 AI 辅助
该研究针对小波MERA框架下的有限BCH多项式纠缠子，发现其存在代数障碍，无法重现伊辛临界性，所有拟设的临界指数β均保持平均场值，需非多项式或无限BCH构造才能实现非平均场临界性。
中文摘要 AI 辅助
将多尺度纠缠重整化拟设（MERA）推广到相互作用量子场论时，非高斯纠缠子的计算处理可能构成重大挑战。因此，自然的策略是考虑多项式纠缠子，其贝克-坎贝尔-豪斯多夫（BCH）展开在有限阶终止。本研究中，我们识别出限制该类纠缠子可访问普适类的代数障碍。在应用于二维相互作用φ⁴理论的小波MERA（wMERA）框架内，我们解析证明，一般情况下任意有限BCH多项式纠缠子产生的有效势必为朗道形式，确立了整个类的平均场普适性；在非一般的简并情形中，所得指数偏离平均场值，但仍无法重现伊辛值。作为数值示例，所考虑的所有拟设中临界指数β始终与平均场值β=1/2一致，且随着非局域范围或变分复杂度增加，无向伊辛值β=1/8漂移。因此，重现非平均场临界性可能需要非多项式或无限BCH构造。
英文摘要
The computational treatment of non-Gaussian entanglers could pose a significant challenge when extending the Multi-Scale Entanglement Renormalization Ansatz (MERA) to interacting quantum field theories. A natural strategy is therefore to consider polynomial entanglers for which the Baker-Campbell-Hausdorff (BCH) expansion terminates at finite order. In this work, we identify an algebraic obstruction that limits the universality classes accessible to this family of entanglers. Working within the wavelet MERA (wMERA) framework applied to the interacting $ϕ^4$ theory in two dimensions, we show analytically that the effective potential generated by any finite-BCH polynomial entangler is necessarily of Landau form in the generic case, establishing mean-field universality for the full class; in non-generic, degenerate cases the resulting exponent departs from mean-field but still fails to reproduce the Ising value. As a numerical illustration, the critical exponent $β$ remains consistent with its mean-field value $β= 1/2$ across all ansätze considered, with no drift toward the Ising value $β= 1/8$ as the nonlocality range or variational complexity increases. Reproducing non-mean-field criticality therefore might require non-polynomial or infinite-BCH constructions.
