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Mass gaps of a $\mathbb{Z}_3$ gauge theory with three fermion flavors in 1 + 1 dimensions
High Energy Physics - Theory · Submitted 27 Oct 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively.
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The abstract, sentence by sentence
We consider a $\mathbb{Z}_3$ gauge theory coupled to three degenerate massive flavors of fermions, which we term "QZD". The spectrum can be computed in $1+1$ dimensions using tensor networks. In weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial, analogous to those of non-relativistic QED in 1+1 dimensions. In strong coupling, besides the usual baryon, the singlet meson is a baryon anti-baryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider a $\mathbb{Z}_3$ gauge theory coupled to three degenerate massive flavors of fermions, which we term "QZD". | contribution 0.90 | 0.65 | 0.04 | asserted 0.93 |
| s1 | The spectrum can be computed in $1+1$ dimensions using tensor networks. | method 0.99 | 0.36 | 0.04 | asserted 0.97 |
| s2 | In weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial, analogous to those of non-relativistic QED in 1+1 dimensions. | result 0.99 | 0.66 | 0.11 | asserted 1.00 |
| s3 | In strong coupling, besides the usual baryon, the singlet meson is a baryon anti-baryon state. | result 1.00 | 0.81 | 0.24 | asserted 1.00 |
| s4 | For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively. | result 1.00 | 0.85 | 0.27 | asserted 1.00 |
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The paper
Original abstract
We consider a $\mathbb{Z}_3$ gauge theory coupled to three degenerate massive flavors of fermions, which we term "QZD". The spectrum can be computed in $1+1$ dimensions using tensor networks. In weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial, analogous to those of non-relativistic QED in 1+1 dimensions. In strong coupling, besides the usual baryon, the singlet meson is a baryon anti-baryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively.
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References
How the literature uses it
6 arXiv papers cite this in 7 sentences
Papers citing it · 5 sentences without a confident label
Cites it as background 2 papers
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While with the numerical approach both abelian [ref] and non-abelian [ref] lattice gauge theory models have been theoretically studied, early demonstrations of quantum simulation of LGT largely focused on abelian theories [ref] .
Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits · Introduction · 0.85
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Finally, beyond pure gauge, approximating QCD requires incorporating fermion fields [ref] .
Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma(36\times3)$ · Outlook · 0.85
What it cites · 37 sentences without a confident label
Uses the method or tool of 3 papers
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Tensor networks [ref] and the Density Matrix Renormalization Group (DMRG) are then used to compute the mass spectrum.
A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States · Introduction · 0.97
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Tensor networks [ref] and the Density Matrix Renormalization Group (DMRG) are then used to compute the mass spectrum.
The ITensor Software Library for Tensor Network Calculations · Introduction · 0.97
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Tensor networks [ref] and the Density Matrix Renormalization Group (DMRG) are then used to compute the mass spectrum.
Tensor lattice field theory with applications to the renormalization group and quantum computing · Introduction · 0.97
Compares with 3 papers
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We also show the prediction of [ref] with dotted lines.
Asymptotic properties of mass spectrum in 't Hooft's model of mesons · DMRG spectra · 0.95
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While the variables are similar to the implementation of a 1 gauge theory by quantum links [ref] , Gauss' law is different, as the flux is only conserved modulo 3.
Quantum Link Models: A Discrete Approach to Gauge Theories · QZD and its weak and strong coupling limit · 0.81
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While the variables are similar to the implementation of a 1 gauge theory by quantum links [ref] , Gauss' law is different, as the flux is only conserved modulo 3.
QCD as a Quantum Link Model · QZD and its weak and strong coupling limit · 0.81
Cites as background 67 papers
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Lastly, Farrell et al. [ref] directly integrated out the N_c gauge fields, which is possible in $1+1$ dimensions, to obtain the mass spectrum for 3 gauge fields coupled to two massive flavors.
Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (I) Axial Gauge · Introduction · 0.85
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A N_c gauge theory coupled to $N_f$ light flavors of quarks can be analyzed using conformal field theory, as a type of Wess-Zumino-Novikov-Witten model [ref] ; it behaves in a manner characteristic of such two dimensional theories.
When cold, dense quarks in 1+1 and 3+1 dimensions are not a Fermi liquid · Introduction · 0.90
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As a N_c gauge theory, the 't Hooft model has baryons, but their properties are opaque [ref] .
Solving two-dimensional large-N QCD with a nonzero density of baryons and arbitrary quark mass · Introduction · 0.87
Discussion
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