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Snowmass White Paper: Hamiltonian Truncation
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abstract
Strongly-coupled Quantum Field Theories (QFTs) are ubiquitous in high energy physics and many-body physics, yet our ability to do precise computations in such systems remains limited. Hamiltonian Truncation is a method for doing nonperturbative computations of real-time evolution in strongly coupled QFT in the continuum limit, and works by numerically solving the Schrodinger equation in a truncated subspace of the full Hilbert space. Recent advances in understanding this method have opened the door to progress in a range of applications, from gauge theories in $d\ge 2$ dimensions to relativistic nonequilibrium physics.
Forward citations
Cited by 6 Pith papers
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QFT as a set of ODEs: higher dimensions
The authors generalize the AdS₂ flow equations for QFT data to AdS₃ and AdS₄, add crossing-based closure and Padé-accelerated sums, and verify them in free theories.
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Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
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Variational Method in Quantum Field Theory
A variational ansatz built from exact sinh-Gordon vacuum expectation values yields quantitative estimates of the φ⁴ ground-state energy and mass, validated by Borel resummation and truncated-space numerics.
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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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Hamiltonian Truncation of Large $N_f$ QED and Large $N$ Vector-like Theories in $d=2+1$
A lightcone Hamiltonian method diagonalizes large-N vector-like gauge theories in 2+1 dimensions exactly, giving explicit eigenstates, spectral densities, and scattering amplitudes.
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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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