Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
Abstract
We explore the thermodynamics of the 1+1-dimensional Gross-Neveu (GN) model at finite number of fermion flavors Nf, finite temperature and finite chemical potential using lattice field theory. In the limit Nf → ∞ the model has been solved analytically in the continuum. In this limit three phases exist: a massive phase, in which a homogeneous chiral condensate breaks chiral symmetry spontaneously, a massless symmetric phase with vanishing condensate and most interestingly an inhomogeneous phase with a condensate, which oscillates in the spatial direction. In the present work we use chiral lattice fermions (naive fermions and SLAC fermions) to simulate the GN model with 2, 8 and 16 flavors. The results obtained with both discretizations are in agreement. Similarly as for Nf → ∞ we find three distinct regimes in the phase diagram, characterized by a qualitatively different behavior of the two-point function of the condensate field. For Nf = 8 we map out the phase diagram in detail and obtain an inhomogeneous region smaller as in the limit Nf → ∞, where quantum fluctuations are suppressed. We also comment on the existence or absence of Goldstone bosons related to the breaking of translation invariance in 1+1 dimensions.