The diagonalization of quantum field Hamiltonians

Lee, Dean; Salwen, Nathan; Lee, Daniel

doi:10.1016/s0370-2693(01)00197-6

Cited by 42 publications

(64 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, in a series of interesting papers [51,52] (see also [53]) this approach was applied to the massive ϕ 4 theory in d We believe that it is worth revisiting the approach of [51,52] and possibly improve on some of the implementation details. 44 As we mentioned in Sec.…”

Section: Appendix B: Other Hamiltonian Truncation Techniquesmentioning

confidence: 99%

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

2015

View full text Add to dashboard Cite

We show how to perform accurate, nonperturbative and controlled calculations in quantum field theory in d dimensions. We use the truncated conformal space approach, a Hamiltonian method which exploits the conformal structure of the UV fixed point. The theory is regulated in the IR by putting it on a sphere of a large finite radius. The quantum field theory Hamiltonian is expressed as a matrix in the Hilbert space of conformal field theory states. After restricting ourselves to energies below a certain UV cutoff, an approximation to the spectrum is obtained by numerical diagonalization of the resulting finite-dimensional matrix. The cutoff dependence of the results can be computed and efficiently reduced via a renormalization procedure. We work out the details of the method for the ϕ 4 theory in d dimensions with d being not necessarily integer. A numerical analysis is then performed for the specific case d ¼ 2.5, a value chosen in the range where UV divergences are absent. By going from weak to intermediate to strong coupling, we are able to observe the symmetry-preserving, symmetry-breaking, and conformal phases of the theory, and perform rough measurements of masses and critical exponents. As a byproduct of our investigations we find that both the free and the interacting theories in nonintegral d are not unitary, which however does not seem to cause much effect at low energies.

show abstract

Section: Appendix B: Other Hamiltonian Truncation Techniquesmentioning

confidence: 99%

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

2015

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…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%

A conformal truncation framework for infinite-volume dynamics

Katz

Khandker

Walters

2016

J. High Energ. Phys.

107

View full text Add to dashboard Cite

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.

show abstract

The diagonalization of quantum field Hamiltonians

Cited by 42 publications

References 15 publications

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

Truncated conformal space approach inddimensions: A cheap alternative to lattice field theory?

The renormalized Hamiltonian truncation method in the large E T expansion

A conformal truncation framework for infinite-volume dynamics

Contact Info

Product

Resources

About