2020年3月1日
Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion
Progress of Theoretical and Experimental Physics
- ,
- 巻
- 2020
- 号
- 3
- 開始ページ
- 033B03
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1093/ptep/ptaa003
- 出版者・発行元
- Oxford University Press (OUP)
<title>Abstract</title>
We develop a $(1+1)$D lattice $U(1)$ gauge theory in order to define the two-flavor massless Schwinger model, and discuss its connection with the Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, by $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{\overline{V } }$, prohibits additive mass renormalization. Moreover, we show that the Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so a Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we show that this lattice model has a mixed ’t Hooft anomaly between $U(1)_{\overline{V } }$, lattice translation, and lattice rotation. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of the Haldane conjecture. Furthermore, it gives a new and strict understanding on the parity-broken phase (Aoki phase) of the $2$D Wilson fermion.
We develop a $(1+1)$D lattice $U(1)$ gauge theory in order to define the two-flavor massless Schwinger model, and discuss its connection with the Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, by $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{\overline{V } }$, prohibits additive mass renormalization. Moreover, we show that the Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so a Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we show that this lattice model has a mixed ’t Hooft anomaly between $U(1)_{\overline{V } }$, lattice translation, and lattice rotation. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of the Haldane conjecture. Furthermore, it gives a new and strict understanding on the parity-broken phase (Aoki phase) of the $2$D Wilson fermion.
- リンク情報
- ID情報
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- DOI : 10.1093/ptep/ptaa003
- eISSN : 2050-3911
- arXiv ID : arXiv:1910.09604