Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion

Yuya Shimizu (RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 650-0047, Japan) ; Yoshinobu Kuramashi (Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan; RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 650-0047, Japan)

We have made a detailed study of the phase structure for the lattice Schwinger model with one flavor of Wilson fermion on the (m,g) plane. For numerical investigation, we develop a decorated tensor renormalization method for lattice gauge theories with fermions incorporating the Grassmann tensor renormalization. Our algorithm manifestly preserves rotation and reflection symmetries. We find not only a parity-broken phase but also a Berezinskii-Kosterlitz-Thouless (BKT) transition by evaluating the central charge and an expectation value of a projection operator into the parity-odd subspace. The BKT phase boundaries converge into the degenerated doubler pole (m,g)=(2,0), while the parity-breaking transition line ends at the physical pole (m,g)=(0,0). In addition, our analysis of scaling dimensions indicates that a conformal field theory with SU(2) symmetry arises on the line of m=2.

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      "title": "Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion"
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  "abstracts": [
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      "source": "APS", 
      "value": "We have made a detailed study of the phase structure for the lattice Schwinger model with one flavor of Wilson fermion on the <math><mrow><mo>(</mo><mi>m</mi><mo>,</mo><mi>g</mi><mo>)</mo></mrow></math> plane. For numerical investigation, we develop a decorated tensor renormalization method for lattice gauge theories with fermions incorporating the Grassmann tensor renormalization. Our algorithm manifestly preserves rotation and reflection symmetries. We find not only a parity-broken phase but also a Berezinskii-Kosterlitz-Thouless (BKT) transition by evaluating the central charge and an expectation value of a projection operator into the parity-odd subspace. The BKT phase boundaries converge into the degenerated doubler pole <math><mo>(</mo><mi>m</mi><mo>,</mo><mi>g</mi><mo>)</mo><mo>=</mo><mo>(</mo><mo>\u2212</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>)</mo></math>, while the parity-breaking transition line ends at the physical pole <math><mo>(</mo><mi>m</mi><mo>,</mo><mi>g</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math>. In addition, our analysis of scaling dimensions indicates that a conformal field theory with SU(2) symmetry arises on the line of <math><mi>m</mi><mo>=</mo><mo>\u2212</mo><mn>2</mn></math>."
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Published on:
06 February 2018
Publisher:
APS
Published in:
Physical Review D , Volume 97 (2018)
Issue 3
DOI:
https://doi.org/10.1103/PhysRevD.97.034502
arXiv:
1712.07808
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: