Non-Hermitian bosonic chains with symmetric hopping can host k-local charges for selected k only, providing counterexamples to all-or-nothing integrability and showing the Grabowski-Mathieu 3-local test is not universal.
Affleck, Universal term in the free energy at a critical point and the conformal anomaly, Phys
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The scheme-independent 3-sphere free energy decreases at O(g^2) under relevant deformations of a 3D CFT but is not monotone along the full RG flow of the free massive scalar on S^3.
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Violating the All-or-Nothing Picture of Local Charges in Non-Hermitian Bosonic Chains
Non-Hermitian bosonic chains with symmetric hopping can host k-local charges for selected k only, providing counterexamples to all-or-nothing integrability and showing the Grabowski-Mathieu 3-local test is not universal.
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The scheme independent 3-sphere free energy is not a monotone F-function
The scheme-independent 3-sphere free energy decreases at O(g^2) under relevant deformations of a 3D CFT but is not monotone along the full RG flow of the free massive scalar on S^3.