A study of lattice gauge theory with next-to-nearest neighbour interaction with the Wilson fermion from a 1/d expansion

1986 ◽  
Vol 271 (3-4) ◽  
pp. 442-460
Author(s):  
Satchidananda Naik
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Nearest Neighbour ◽  
Wilson Fermion ◽  
Lattice Gauge ◽  
Neighbour Interaction

scholarly journals Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Tatsuhiro Misumi ◽  
Yuya Tanizaki
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Fine Tuning ◽  
Lattice Rotation ◽  
Dirac Fermions ◽  
Wilson Fermion ◽  
Schwinger Model ◽  
Lattice Gauge ◽  
Sign Problem ◽  
The Continuum

Abstract 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.

Chiral properties of the Wilson fermion in SU(2) lattice gauge theory

1983 ◽  
Vol 130 (3-4) ◽  
pp. 199-204 ◽  
Author(s):  
M. Fukugita ◽  
T. Kaneko ◽  
A. Ukawa
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Wilson Fermion ◽  
Lattice Gauge

scholarly journals Thermal phase transition in mixed action SU (3) lattice gauge theory and Wilson fermion thermodynamics

1995 ◽  
Vol 442 (1-2) ◽  
pp. 301-316 ◽  
Author(s):  
T. Blum ◽  
C. DeTar ◽  
Urs M. Heller ◽  
Leo Kärkkäinen ◽  
K. Rummukainen ◽  
...  
Keyword(s):  
Phase Transition ◽  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Wilson Fermion ◽  
Lattice Gauge ◽  
Thermal Phase Transition ◽  
Thermal Phase ◽  
Mixed Action
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