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Exploring Hamiltonian Truncation in $\bf{d=2+1}$
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abstract
We initiate the application of Hamiltonian Truncation methods to solve strongly coupled QFTs in $d=2+1$. By analysing perturbation theory with a Hamiltonian Truncation regulator, we pinpoint the challenges of such an approach and propose a way that these can be addressed. This enables us to formulate Hamiltonian Truncation theory for $\phi^4$ in $d=2+1$, and to study its spectrum at weak and strong coupling. The results obtained agree well with the predictions of a weak/strong self-duality possessed by the theory. The $\phi^4$ interaction is a strongly relevant UV divergent perturbation, and represents a case study of a more general scenario. Thus, the approach developed should be applicable to many other QFTs of interest.
Forward citations
Cited by 4 Pith papers
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Toolkit for General 2d Scalar Potential in LCT
An efficient LCT toolkit confirms the sinh-Gordon self-duality and reproduces the sine-Gordon spectrum, c-function, and free fermion limit with high precision.
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Higher-order structure of Hamiltonian truncation effective theory
All-order local and O(Emax⁻⁴) non-local corrections are derived for Hamiltonian truncation effective theory of 2D λφ⁴; numerically, NNLO barely improves on NLO.
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Systematic Improvement of Hamiltonian Truncation Effective Theory
NLO matching corrections with nonlocal terms are computed for 1+1D λφ⁴ Hamiltonian truncation, and the eigenvalue error is shown to scale as 1/Emax⁴, confirming the effective theory power counting.
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Testing the RG-flow $M(3,10)+\phi_{1,7}\to M(3,8)$ with Hamiltonian Truncation
Hamiltonian truncation with counterterms through third order supports the conjectured RG flow M(3,10)+φ_{1,7}→M(3,8), though the evidence is fit-based and not fully converged.
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