Spectroscopy in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mi mathvariant="normal">D</mml:mi></mml:mrow></mml:math> Thirring model with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> domain wall fermions

We employ the domain wall fermion (DWF) formulation of Thirring model on a lattice in $2+1+1$ dimensions and perform $N=1$ flavor Monte Carlo simulations. At critical interaction strength features spontaneous $\mathrm{U}(2)\ensuremath{\rightarrow}\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{U}(1)$ symmetry breaking; we analyze induced spin-0 mesons, both Goldstone non-Goldstone, as well correlator quasiparticles, resulting phases. Crucially, determine anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\psi}}\ensuremath{\approx}3$ at point, stark contrast with Gross-Neveu 3D results obtained staggered fermions. Our numerical simulations are complemented by an analytical treatment free correlator, which exhibits large early-time artifacts due to branch cuts propagator stemming from unbound interactions its heavy doublers. These generalizable beyond model, being intrinsic property DWF, or more generally Ginsparg-Wilson