Hamiltonian truncation study of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>theory in two dimensions

Rychkov, Slava; Vitale, Lorenzo G.

doi:10.1103/physrevd.91.085011

Cited by 137 publications

(329 citation statements)

References 40 publications

Supporting

Mentioning

310

Contrasting

Order By: Relevance

“…This is what was done in the previous works [17][18][19], where (11) was truncated to the leading order (LO) n = 2, and ∆H 2 was computed in an analytic local approximation…”

Section: Jhep10(2017)213mentioning

confidence: 99%

“…As a result the convergence is improved. Renormalized HT has been applied in several strongly coupled QFT studies in d = 2 [18][19][20][21]24] and in one study in d = 2.5 [17]. We hope that in the future Hamiltonian Truncation will develop into an accurate numerical method, applicable also in d 3.…”

Section: Jhep10(2017)213mentioning

confidence: 99%

“…We stress however that the basic ideas of NLO-HT and of its implementation described below are general and can be used for many other theories. We introduce here the (φ 4 ) 2 theory very briefly; see [18,25] for details. The theory is defined by the normal-ordered Euclidean action…”

Section: Jhep10(2017)213mentioning

confidence: 99%

“…Motivated by the need to mitigate the above limitations, the recent works [17][18][19][20] (following notably [21]; see also [22][23][24]) started developing the theory of renormalized HT, 1 In relativistic QFTs one can also quantize on surfaces of constant light-cone coordinate. 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].…”

Section: Jhep10(2017)213mentioning

confidence: 99%

“…On the other hand, the matrix ∆H > 2 involves an infinite sum over the states with E i > E L , for which we use a local approximation [17,18]:…”

Section: Jhep10(2017)213mentioning

confidence: 99%

See 4 more Smart Citations

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.

Self Cite

View full text Add to dashboard Cite

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...

show abstract

“…This is what was done in the previous works [17][18][19], where (11) was truncated to the leading order (LO) n = 2, and ∆H 2 was computed in an analytic local approximation…”

Section: Jhep10(2017)213mentioning

confidence: 99%

Section: Jhep10(2017)213mentioning

confidence: 99%

Section: Jhep10(2017)213mentioning

confidence: 99%

Section: Jhep10(2017)213mentioning

confidence: 99%

“…On the other hand, the matrix ∆H > 2 involves an infinite sum over the states with E i > E L , for which we use a local approximation [17,18]:…”

Section: Jhep10(2017)213mentioning

confidence: 99%

See 3 more Smart Citations

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.

Self Cite

View full text Add to dashboard Cite

show abstract

Untitled

Chabysheva¹

2017

Light Cone 2015

View full text Add to dashboard Cite

We extend earlier work on fully symmetric polynomials for three-boson wave functions to arbitrarily many bosons and apply these to a light-front analysis of the low-mass eigenstates of φ 4 theory in 1+1 dimensions. The basis-function approach allows the resolution in each Fock sector to be independently optimized, which can be more efficient than the preset discrete Fock states in DLCQ. We obtain an estimate of the critical coupling for symmetry breaking in the positive mass-squared case.a Based on a talk contributed to the Lightcone 2015 workshop, Frascati, Italy, September 21-25, 2015.

show abstract

Untitled

Chabysheva¹

2018

Light Cone 2016

View full text Add to dashboard Cite

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.

show abstract

Hamiltonian truncation study of theφ4theory in two dimensions

Cited by 137 publications

References 40 publications

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

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

Untitled

Untitled

Contact Info

Product

Resources

About