Numerical study of the 2+1d Thirring Model with U(2N)-invariant fermions
In 2+1 dimensions the global U(2$N$) symmetry associated with massless fermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I will show how to adapt the domain wall formulation to recover the U(2$N$)-invariant limit in interacting fermion models as the domain wall operation is increased. In particular, I will focus on the issue of potential dynamical mass generation in the Thirring model, postulated to take place for $N$ less than some critical $N_c$. I will present results of simulations of the model using both HMC ($N$=2) and RHMC ($N$=1) algorithms, and show that the outcome is very different from previous numerical studies of the model made with staggered fermions, where the corresponding pattern of symmetry breaking is distinct.
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