Hamiltonian truncation is a numerical method used to study quantum field theories (QFTs) in spacetime dimensions. Hamiltonian truncation is an adaptation of the Rayleigh–Ritz method from quantum mechanics. It is closely related to the exact diagonalization method used to treat spin systems in condensed matter physics.[1] The method is typically used to study QFTs on spacetimes of the form , specifically to compute the spectrum of the Hamiltonian along . A key feature of Hamiltonian truncation is that an explicit ultraviolet cutoff is introduced, akin to the lattice spacing a in lattice Monte Carlo methods. Since Hamiltonian truncation is a nonperturbative method, it can be used to study strong-coupling phenomena like spontaneous symmetry breaking.
^Whitsitt, Seth; Schuler, Michael; Henry, Louis-Paul; Läuchli, Andreas M.; Sachdev, Subir (2017-07-24). "Spectrum of the Wilson-Fisher conformal field theory on the torus". Physical Review B. 96 (3). American Physical Society (APS): 035142. arXiv:1701.03111. Bibcode:2017PhRvB..96c5142W. doi:10.1103/physrevb.96.035142. ISSN 2469-9950. S2CID 119336211.
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Hamiltoniantruncation is a numerical method used to study quantum field theories (QFTs) in d ≥ 2 {\displaystyle d\geq 2} spacetime dimensions. Hamiltonian...
{2}}{6}}a^{3}} Because six pyramids are removed by truncation, there is a total lost volume of √2a3. The truncated octahedron has five special orthogonal projections...
edge truncation of the tetrahedron. The truncated triangular trapezohedron is another polyhedron which can be formed from cube edge truncation. The truncated...
Hamiltonian simulation (also referred to as quantum simulation) is a problem in quantum information science that attempts to find the computational complexity...
does not contain triangles or squares. In general usage, the degree of truncation is assumed to be uniform unless specified. It has 12 regular pentagonal...
molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei...
be constructed by truncating all 4 vertices of a regular tetrahedron at one third of the original edge length. A deeper truncation, removing a tetrahedron...
In geometry, a truncated icosidodecahedron, rhombitruncated icosidodecahedron, great rhombicosidodecahedron, omnitruncated dodecahedron or omnitruncated...
of a truncation process between a dodecahedron and icosahedron: This polyhedron is topologically related as a part of sequence of uniform truncated polyhedra...
In geometry, the truncated cuboctahedron or great rhombicuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron. It...
theory uses the difference between the Hartree–Fock Hamiltonian and the exact non-relativistic Hamiltonian as the perturbation. The zero-order energy is the...
attempts to find the lowest-energy matrix product state wavefunction of a Hamiltonian. It was invented in 1992 by Steven R. White and it is nowadays the most...
descriptions as a fallback Hamiltonian constraint – Key constraint in some theories admitting Hamiltonian formulations Hamiltonian constraint of LQG – Constraint...
defined by duality and its dual operation, truncation: the Kleetope of P is the dual polyhedron of the truncation of the dual of P. If P has enough vertices...
by vertex figure n3. The regular dodecahedron can be transformed by a truncation sequence into its dual, the icosahedron: The regular dodecahedron is a...
energy of a configuration σ {\displaystyle {\sigma }} is given by the Hamiltonian function H ( σ ) = − ∑ ⟨ i j ⟩ J i j σ i σ j − μ ∑ j h j σ j , {\displaystyle...
eigenvalues (energy levels) with the classical behavior of the same Hamiltonian (system). Study of probability distribution of individual eigenstates...
solved on this basis, using an effective Hamiltonian specifically suited for the model space. This Hamiltonian is different from the one of free nucleons...
in the Hamiltonian to play the role of the tunneling field (kinetic part). Then one may carry out the simulation with the quantum Hamiltonian thus constructed...
coefficient vector, e is the eigenvalue matrix, and the elements of the hamiltonian and overlap matrices are, respectively, H i j = ⟨ Φ i S O | H e l | Φ...
compound of two snub dodecahedra, and the convex hull of both forms is a truncated icosidodecahedron. Kepler first named it in Latin as dodecahedron simum...
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