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Chabysheva, Sophia S.

doi:10.1007/978-3-319-50699-9_50

Cited by 3 publications

(5 citation statements)

References 20 publications

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“…We can confirm this IR cutoff structure by instead plotting the one-particle mass shift as a function of the ratio 12) which is shown in figure 12 for multiple values of k max with ∆ max = 13. As we can see, for large Λ IR the plots all collapse to a single curve.…”

Section: Jhep07(2016)140mentioning

confidence: 76%

“…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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Section: Jhep07(2016)140mentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

A conformal truncation framework for infinite-volume dynamics

Katz

Khandker

Walters

2016

J. High Energ. Phys.

107

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“…When the Fockspace truncation is removed, in the N max → ∞ limit, the dimensionless sector-dependent mass μm becomes μ ≡ ±4πµ 2 /λ. This convergence to the sector-independent mass happens first in the lowest sector; therefore, the dimensionless coupling g ≡ λ 4πµ 2 can be extracted as g ≃ 1/|μ 2 1 | and the dimensionless eigenmass as M 2 /µ 2 = g M2 = M2 /|μ 2 1 |. The sector-dependent case is no longer an explicit eigenvalue problem.…”

Section: Sector-dependent Constituent Massmentioning

confidence: 96%

“…Previous calculations [1,2] have shown that there is a systematic difference between light-front and equal-time values for the critical coupling of φ 4 theory. Here we discuss the resolution of this by considering the difference in mass renormalizations as originally suggested by Burkardt [3].…”

Section: Introductionmentioning

confidence: 96%

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Chabysheva¹

2018

Light Cone 2016

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There is a discrepancy between light-front and equal-time values for the critical coupling of twodimensional φ 4 theory. A proposed resolution is to take into account the difference between mass renormalizations in the two quantizations. This distinction was first discussed by M. Burkardt. It prevents direct comparison of bare parameters; however, a method proposed here allows calculation of the difference and thereby resolves the discrepancy. We also consider the consequences of allowing a sector-dependent constituent mass.a Based on a talk contributed to the Lightcone 2016 workshop, Lisbon, Portugal, September 5-8, 2016.

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“…This light front quantization [9] is also used in numerical solutions of strongly coupled QFTs via a version of HT; some recent work is [10][11][12][13][14][15]. The structure of the unperturbed Hilbert space is different from the equal time case, which leads to important differences in the numerical procedure.…”

Section: Jhep10(2017)213mentioning

confidence: 99%

High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian Truncation

Elias-Miró

Vitale

Rychkov

2017

J. High Energ. Phys.

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Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d = 2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d 3. Keywords: Field Theories in Lower Dimensions, Nonperturbative EffectsArXiv ePrint: 1706.06121Open Access, c The Authors. Article funded by SCOAP 3 .https://doi.org/10.1007/JHEP10 (2017)213 JHEP10 (2017)213 Introduction. Many interesting strongly interacting Quantum Field Theories (QFTs) are not amenable to analytical treatment. Such theories are often studied via Lattice Monte Carlo (LMC) numerical simulations, starting from the discretized Euclidean action. However, LMC has some drawbacks, for example it cannot easily compute real-time observables, it is rather computationally expensive, and it cannot directly describe renormalization group (RG) flows starting from interacting fixed points. Therefore, it is worth exploring other numerical approaches to strongly interacting QFTs. One promising alternative is provided by the Hamiltonian methods, which look for the eigenstates of the quantum Hamiltonian. These methods use various finite-dimensional approximations to the full infinite-dimensional QFT Hilbert space. Notable examples are the methods using Matrix Product States [1, 2] and more general Tensor Networks [3] such as MERA [4] or PEPS [5]. In this paper we will be concerned with another representative of this group of methods -Hamiltonian Truncation (HT), also known as the Truncated Spectrum (or Space) Approach, which is a direct generalization of the variational Rayleigh-Ritz (RR) method from quantum mechanics. This method goes back to the seminal work of Yurov and Al. Zamolodchikov [6,7] and has since been applied in many contexts. See [8] for a recent extensive review and the bibliography.The idea of HT is simple. The QFT Hamiltonian operator H is split as H 0 + V where H 0 is an exactly solvable Hamiltonian whose eigenstates form the basis of the Hilbert space. One quantizes at surfaces of constant time and works in finite volume so that the spectrum is discrete. 1 The Hilbert space is then truncated to the low-lying eigenvectors of H 0 . The matrix of H in this truncated Hilbert space is diagonalized exactly on a computer, to find the low-energy spectrum of interacting eigenstates.As was understood early on [16], the numerical convergence of the HT...

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Cited by 3 publications

References 20 publications

A conformal truncation framework for infinite-volume dynamics

A conformal truncation framework for infinite-volume dynamics

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High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian Truncation

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