Scalars coupled to fermions in 1+1 dimensions

Brooks, Eugene D.; Frautschi, Steven C.

doi:10.1007/bf01546194

Cited by 23 publications

(36 citation statements)

References 2 publications

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“…Two broad categories within the Hamiltonian truncation methods are the Truncated Conformal Space Approach [4] and Discrete Light Cone Quantization [5]. A less traveled route consists in using the Fock-Space basis to truncate the Hamiltonian [1,2,[6][7][8][9][10]. Lately there have been many advances in the Hamiltonian Truncation methods, see for instance [3,[11][12][13][14][15][16][17].…”

Section: Jhep04(2016)144mentioning

confidence: 99%

The renormalized Hamiltonian truncation method in the large E T expansion

Elias-Miró

Montull

Riembau

2016

J. High Energ. Phys.

176

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Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by . The method is general but as an example we calculate the exact g 2 and some of the g 3 contributions for the φ 4 theory in two dimensions. The coefficients of the local expansion calculated in ref.[1] are shown to be given by phase space integrals. In addition we find new approximations to speed up the numerical calculations and implement them to compute the lowest energy levels at strong coupling. A simple diagrammatic representation of the corrections and various tests are also introduced.

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Section: Jhep04(2016)144mentioning

confidence: 99%

The renormalized Hamiltonian truncation method in the large E T expansion

Elias-Miró

Montull

Riembau

2016

J. High Energ. Phys.

176

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“…Note that this regulator is Lorentz invariant and preserves the conformal structure of the basis, in that it does not mix states with different Casimir eigenvalue. In the simple case of a scalar operator, this regulator defines the inner product 5) where ρ O (µ) is the spectral density of the operator O(x). Our polynomials are orthogonal with respect to this inner product.…”

Section: Jhep07(2016)140mentioning

confidence: 99%

“…Given this choice, we see that diagonalizing the operator M 2 is equivalent to diagonalizing the lightcone Hamiltonian P + . Since the UV theory is free, we can expand the massless scalar field φ in terms of the usual Fock space modes, 5) where the creation and annihilation operators a † and a satisfy the commutation relation…”

Section: Lightcone Hamiltonianmentioning

confidence: 99%

“…The Hamiltonian correction due to the mass term, 5) JHEP07 (2016)140 leads to the two-particle M 2 matrix elements,…”

Section: Two-particle Statesmentioning

confidence: 99%

“…It is therefore a worthwhile goal to search for non-perturbative methods which may also access dynamical observables. Hamiltonian truncation has recently gained momentum as a means of studying realtime dynamics [1][2][3][4][5][6][7][8][9][10][11][12][13]. The basic idea is to first discretize the QFT in some manner, yielding a Hilbert space consisting of an infinite tower of discrete basis states.…”

Section: Introductionmentioning

confidence: 99%

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A conformal truncation framework for infinite-volume dynamics

Katz

Khandker

Walters

2016

J. High Energ. Phys.

107

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We present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, P , and conformal Casimir, C. The relevant deformation is then considered using lightcone quantization, with the resulting Hamiltonian expressed in terms of this CFT basis. Truncating to states with C ≤ C max , one can numerically find the resulting spectrum, as well as other dynamical quantities, such as spectral densities of operators. This method requires the introduction of an appropriate regulator, which can be chosen to preserve the conformal structure of the basis. We check this framework in three dimensions for various perturbative deformations of a free scalar CFT, and for the case of a free O(N ) CFT deformed by a mass term and a non-perturbative quartic interaction at large-N . In all cases, the truncation scheme correctly reproduces known analytic results. We also discuss a general procedure for generating a basis of Casimir eigenstates for a free CFT in any number of dimensions.

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On a numerical exact solution to the many-body problem in one dimension

Pauli

1984

Z Physik A

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The Hamiltonian matrix for up to 30 particles has been diagonalised for three different interactions in a plane wave base, among them a hard-core potential. Restriction was made to the spin-polarised case in one space dimension. In the present feasibility study much weight is placed on the questions of convergence, numerical stability and efficiency. Some selected results on binding energies, excitation spectra, momentum distributions and spatial correlation functions are presented and discussed.

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Scalars coupled to fermions in 1+1 dimensions

Cited by 23 publications

References 2 publications

The renormalized Hamiltonian truncation method in the large E T expansion

The renormalized Hamiltonian truncation method in the large E T expansion

A conformal truncation framework for infinite-volume dynamics

On a numerical exact solution to the many-body problem in one dimension

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