Truncated Hilbert space approach to the 2d $\phi^{4}$ theory

Bajnok, Zoltan; Lajer, Marton

doi:10.1007/JHEP10(2016)050

Truncated Hilbert space approach to the 2d $\phi^{4}$ theory

Zoltan Bajnok
(
- Wigner RCP, Budapest
)
,
Marton Lajer
(
- Eotvos U.
)

Dec 21, 2015

29 pages

Published in:

JHEP 10 (2016) 050

Published: Oct 11, 2016

e-Print:

1512.06901 [hep-th]

DOI:

10.1007/JHEP10(2016)050

View in:

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Abstract: (Springer)

We apply the massive analogue of the truncated conformal space approach to study the two dimensional ϕ

^{4}

theory in finite volume. We focus on the broken phase and determine the finite size spectrum of the model numerically. We interpret the results in terms of the Bethe-Yang spectrum, from which we extract the infinite volume masses and scattering matrices for various couplings. We compare these results against semiclassical analysis and perturbation theory. We also analyze the critical point of the model and confirm that it is in the Ising universality class.

Note:

pdflatex, 35 pages with 29 pdf figures. Binary program is also attached, run on linux as: phi4 config.dat, v2: typos corrected, comparison to other works and references added, vacuum splitting analysis corrected, comparison to sine-Gordon TCSA added, v3: improved numerics, analysis on excited kink added, critical point investigated

Field Theories in Lower Dimensions
Nonperturbative Effects
Hilbert space
space: conformal
field theory: conformal
dimension: 2
finite size
semiclassical

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Figures(24)

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Truncated Hilbert space approach to the 2d ϕ4\phi^{4}ϕ4 theory

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Truncated Hilbert space approach to the 2d $\phi^{4}$ theory