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Chiral Symmetry Breaking on the Lattice: a Study of the Strongly Coupled Lattice Schwinger Model
High Energy Physics - Lattice · Submitted 18 Oct 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that this discrete symmetry is indeed broken spontaneously in the strong coupling li mit.
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The abstract, sentence by sentence
We revisit the strong coupling limit of the Schwinger model on the lattice using staggered fermions and the hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they posses a discrete axial invari ance which forbids fermion mass and which must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory. We show that this discrete symmetry is indeed broken spontaneously in the strong coupling li mit. Expanding around a gauge invariant ground state and carefully considering the normal ordering of the charge operator, we derive an improved strong coupling expansion and compute the masses of the low lying bosonic excitations as well as the chiral co ndensate of the model. We find very good agreement between our lattice calculations and known continuum values for these quantities already in the fourth order of strong coupling perturbation theory. We also find the exact ground state of the antiferromag netic Ising spin chain with long range Coulomb interaction, which determines the nature of the ground state in the strong coupling limit.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We revisit the strong coupling limit of the Schwinger model on the lattice using staggered fermions and the hamiltonian approach to lattice gauge theories. | contribution 0.69 | 0.88 | 0.03 | asserted 0.77 |
| s1 | Although staggered fermions have no continuous chiral symmetry, they posses a discrete axial invari ance which forbids fermion mass and which must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory. | background 1.00 | 0.08 | 0.07 | asserted 1.00 |
| s2 | We show that this discrete symmetry is indeed broken spontaneously in the strong coupling li mit. | result 0.99 | 0.93 | 0.60 | asserted 1.00 |
| s3 | Expanding around a gauge invariant ground state and carefully considering the normal ordering of the charge operator, we derive an improved strong coupling expansion and compute the masses of the low lying bosonic excitations as well as the chiral co ndensate of the model. | method 0.94 | 0.97 | 0.09 | asserted 1.00 |
| s4 | We find very good agreement between our lattice calculations and known continuum values for these quantities already in the fourth order of strong coupling perturbation theory. | result 0.99 | 0.96 | 0.26 | asserted 1.00 |
| s5 | We also find the exact ground state of the antiferromag netic Ising spin chain with long range Coulomb interaction, which determines the nature of the ground state in the strong coupling limit. | result 0.92 | 0.95 | 0.11 | asserted 1.00 |
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Original abstract
We revisit the strong coupling limit of the Schwinger model on the lattice using staggered fermions and the hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they posses a discrete axial invari ance which forbids fermion mass and which must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory. We show that this discrete symmetry is indeed broken spontaneously in the strong coupling li mit. Expanding around a gauge invariant ground state and carefully considering the normal ordering of the charge operator, we derive an improved strong coupling expansion and compute the masses of the low lying bosonic excitations as well as the chiral co ndensate of the model. We find very good agreement between our lattice calculations and known continuum values for these quantities already in the fourth order of strong coupling perturbation theory. We also find the exact ground state of the antiferromag netic Ising spin chain with long range Coulomb interaction, which determines the nature of the ground state in the strong coupling limit.
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4 arXiv papers cite this in 16 sentences
Papers citing it · 6 sentences without a confident label
Contests it 1 paper
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VEVExpanded -a ⟨Ψ̅Ψ⟩= 1/2- 8 y + 288 y^2 - 306688/25 y^3 + O(y^4) The coefficient of $y^2$ does not agree with [ref] (we have checked some of the strong coupling results in [ref] ).
Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model · Strong coupling expansions · contest 0.85
Compares with it 1 paper
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To order $y^2$ this agrees with [ref] .
Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model · Strong coupling expansions · 0.98
Cites it as background 2 papers
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This allows us to make contact with the subsequent work on the lattice Schwinger model, which mostly used the original definition of [ref] rather than the modified definition of [ref] .
Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model · Introduction · 0.90
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This model has been studied previously using both strategies mentioned above (see, for instance, [ref] ), as well as with older methods such as the lattice strong-coupling expansion [ref] .
Infinite matrix product states for $(1+1)$-dimensional gauge theories · Introduction · 0.95
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