An Algebraic Obstruction to Ising Criticality for Finite-BCH Entanglers in Wavelet MERA
Abstract
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 ϕ4 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.
Related
- Finite-temperature quantum Monte Carlo study of Dirac quantum criticality: Algorithmic advances and comprehensive analysis
- Symmetry-permuting entanglers for non-invertible symmetry-protected topological phases
- Topological Obstruction to Forgetting in Finite Distinction Systems: Quotient Invariants, Non-Hermitian Skin Effects, and Topological Side-Ledgers
- Algebraic Structure of Finite-Size Bethe Solutions in the Heisenberg Chain
- Finite-Precision Algebraic Quantum Field Theory: Quantum Parcels, Locality, Modular Structure and Factors
BibTeX
@misc{bertuzzo2026algebraic,
title = {{An Algebraic Obstruction to Ising Criticality for Finite-BCH Entanglers in Wavelet MERA}},
author = {Enrico Bertuzzo and Olindo Corradini and Claudia Frugiuele},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27564},
eprint = {2608.27564},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27564},
}
RIS
TY - UNPB
TI - An Algebraic Obstruction to Ising Criticality for Finite-BCH Entanglers in Wavelet MERA
AU - Enrico Bertuzzo
AU - Olindo Corradini
AU - Claudia Frugiuele
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27564
UR - https://arxiv.org/abs/2608.27564
AB - 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.
ER -