In a recent work [1] we studied the phase structure of the Gross-Neveu (GN) model in 1 + 1 dimensions at finite number of fermion flavors N f = 2, 8, 16, finite temperature and finite chemical potential using lattice field theory. Most importantly, we found an inhomogeneous phase at low temperature and large chemical potential, quite similar to the analytically solvable N f → ∞ limit. In the present work we continue our lattice field theory investigation of the finite-N f GN model by studying the formation of baryons, their spatial distribution and their relation to the chiral condensate. As a preparatory step we also discuss a linear coupling of lattice fermions to the chemical potential.
The Thirring model is an interacting fermion theory with current-current interaction. The model in 1 + 2 dimensions has applications in condensed-matter physics to describe the electronic excitations of Dirac materials. Earlier investigations with Schwinger-Dyson equations, the functional renormalization group and lattice simulations with staggered fermions suggest that a critical number of (reducible) flavors N c exists, below which chiral symmetry can be broken spontaneously. Values for N c found in the literature vary between 2 and 7. Recent lattice studies with chirally invariant SLAC fermions have indicated that chiral symmetry is unbroken for all integer flavor numbers [1,2]. An independent simulation based on domain wall fermions seems to favor a critical flavornumber that satisfies 1 < N c < 2 [3]. However, in the latter simulations difficulties in reaching the massless limit in the broken phase (at strong coupling and after the Ls → ∞ limit has been taken) are encountered. To find an accurate value N c we study the Thirring model (by using an analytic continuation of the parity even theory to arbitrary real N ) for N between 0.5 and 1.1. We investigate the chiral condensate, the spectral density of the Dirac operator, the spectrum of (would-be) Goldstone bosons and the variation of the filling-factor and conclude that the critical flavor number is N c = 0.80(4). Thus we see no chiral symmetry breaking in all Thirring models with 1 or more flavors of (4-component) fermions. Besides the transition to the unphysical lattice artifact phase we find strong evidence for a hitherto unknown phase transition that exists for N > N c and should answer the question of where to construct a continuum limit.
We study the phase diagram of the 1+1 dimensional Gross-Neveu model at finite number of fermion flavors using lattice field theory. Numerical results are presented, which indicate the existence of an inhomogeneous phase, where the chiral condensate is a spatially oscillating function.
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