Spectroscopy in the <math display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn><mi mathvariant="normal">D</mi></mrow></math> Thirring model with <math display="inline"><mi>N</mi><mo>=</mo><mn>1</mn></math> domain wall fermions - INSPIRE

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Spectroscopy in the $2 + 1 D$ Thirring model with $N = 1$ domain wall fermions

Oct 10, 2022

39 pages

Published in:

Phys.Rev.D 107 (2023) 1, 014504

Published: Jan 1, 2023

e-Print:

2210.04790 [hep-lat]

DOI:

10.1103/PhysRevD.107.014504 (publication)

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Abstract: (APS)

We employ the domain wall fermion (DWF) formulation of the Thirring model on a lattice in

2 + 1 + 1

dimensions and perform

N = 1

flavor Monte Carlo simulations. At a critical interaction strength the model features a spontaneous

U (2) \to U (1) \otimes U (1)

symmetry breaking; we analyze the induced spin-0 mesons, both Goldstone and non-Goldstone, as well as the correlator of the fermion quasiparticles, in both resulting phases. Crucially, we determine the anomalous dimension

η_{ψ} \approx 3

at the critical point, in stark contrast with the Gross-Neveu model in 3D and with results obtained with staggered fermions. Our numerical simulations are complemented by an analytical treatment of the free fermion correlator, which exhibits large early-time artifacts due to branch cuts in the propagator stemming from unbound interactions of the fermion with its heavy doublers. These artifacts are generalizable beyond the Thirring model, being an intrinsic property of DWF, or more generally Ginsparg-Wilson fermions.

Note:

27 + 12 pages, 13 + 6 figures; code and data available (https://doi.org/10.17638/datacat.liverpool.ac.uk/1959)

fermion: correlation function
fermion: domain wall
fermion: interaction
fermion: quasiparticle
fermion: staggered
numerical calculations: Monte Carlo
Thirring model
critical phenomena
anomalous dimension
lattice

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