Topological Phase Transitions Beyond Landau: Deconfined Quantum Criticality in 3+1D — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Topological phase transitions transcend Landau's symmetry-breaking paradigm, requiring non-local order parameters and exhibiting deconfined quantum criticality in 3+1D. | MATH: Landau free energy F = F0 + a(T−Tc)ϕ2 + bϕ4 fails for topological transitions; topological invariant Q = 1/2π∮ A· dk (Chern number) replaces local order parameter; deconfined criticality involves emergent gauge fields with coupling g ∼ e2π i/N for N-component matter; non-abelian transitions in 3+1D require higher-form symmetries U(1)[p] with p-dimensional charged objects. | CONNECTION: Topological order maps to **root systems** — e.g., An (SU(n+1)) and Dn (SO(2n)) Lie algebra structures encode braiding statistics; fractionalized excitations carry quantum dimensions dα = (sin(π/(k+2)))/(sin(π/(k+2))) (Fibonacci anyons: d = ϕ = 1.618, golden ratio appears in k=3 S
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026topological,
title = {{Topological Phase Transitions Beyond Landau: Deconfined Quantum Criticality in 3+1D — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635525},
url = {https://zenodo.org/records/23635525},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological Phase Transitions Beyond Landau: Deconfined Quantum Criticality in 3+1D — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635525
UR - https://zenodo.org/records/23635525
AB - FINDING: Topological phase transitions transcend Landau's symmetry-breaking paradigm, requiring non-local order parameters and exhibiting deconfined quantum criticality in 3+1D. | MATH: Landau free energy F = F_0 + a(T−T_c)ϕ^2 + bϕ^4 fails for topological transitions; topological invariant Q = 1/2π∮ A· dk (Chern number) replaces local order parameter; deconfined criticality involves emergent gauge fields with coupling g ∼ e^2π i/N for N-component matter; non-abelian transitions in 3+1D require higher-form symmetries U(1)^[p] with p-dimensional charged objects. | CONNECTION: Topological order maps to **root systems** — e.g., A_n (SU(n+1)) and D_n (SO(2n)) Lie algebra structures encode braiding statistics; fractionalized excitations carry quantum dimensions d_α = (sin(π/(k+2)))/(sin(π/(k+2))) (Fibonacci anyons: d = ϕ = 1.618, golden ratio appears in k=3 S Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -