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Title: RG flow from Φ 4 theory to the 2D Ising model

Abstract

We study 1+1 dimensional Φ 4 theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C≤C max, we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along the full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.

Authors:
 [1];  [2];  [3];  [4];  [3]
  1. Johns Hopkins Univ., Baltimore, MD (United States). Department of Physics and Astronomy
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Mathematics
  3. Boston Univ., MA (United States). Dept. of Physics
  4. Boston Univ., MA (United States). Dept. of Physics ; Univ. of Illinois, Urbana, IL (United States). Department of Physics
Publication Date:
Research Org.:
Boston Univ., MA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1426157
Grant/Contract Number:  
SC0015845
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal Field Theory; Field Theories in Lower Dimensions; Nonperturbative Effects; Renormalization Group

Citation Formats

Anand, Nikhil, Genest, Vincent X., Katz, Emanuel, Khandker, Zuhair U., and Walters, Matthew T. RG flow from Φ 4 theory to the 2D Ising model. United States: N. p., 2017. Web. doi:10.1007/JHEP08(2017)056.
Anand, Nikhil, Genest, Vincent X., Katz, Emanuel, Khandker, Zuhair U., & Walters, Matthew T. RG flow from Φ 4 theory to the 2D Ising model. United States. doi:10.1007/JHEP08(2017)056.
Anand, Nikhil, Genest, Vincent X., Katz, Emanuel, Khandker, Zuhair U., and Walters, Matthew T. Wed . "RG flow from Φ 4 theory to the 2D Ising model". United States. doi:10.1007/JHEP08(2017)056. https://www.osti.gov/servlets/purl/1426157.
@article{osti_1426157,
title = {RG flow from Φ 4 theory to the 2D Ising model},
author = {Anand, Nikhil and Genest, Vincent X. and Katz, Emanuel and Khandker, Zuhair U. and Walters, Matthew T.},
abstractNote = {We study 1+1 dimensional Φ 4 theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C≤Cmax, we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along the full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.},
doi = {10.1007/JHEP08(2017)056},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2017,
place = {United States},
year = {2017},
month = {8}
}

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