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We study the phase diagram of the $(1+1)$-dimensional Gross-Neveu model withboth $g_x^2(\bar{\psi}\psi)^2$ and $g_y^2(\bar{\psi}i\gamma_5\psi)^2$interaction terms on a spatial lattice. The continuous chiral symmetry, whichis present in the continuum model when $g_x^2=g_y^2$, has a mixed 't~Hooftanomaly with the charge conservation symmetry, which guarantees the existenceof a massless mode. However, the same 't~Hooft anomaly also implies that thecontinuous chiral symmetry is broken explicitly in our lattice model.Nevertheless, from numerical matrix product state simulations we find that, forcertain parameters of the lattice model, the continuous chiral symmetryreemerges in the infrared fixed point theory, even at strong coupling. We arguethat, to understand this phenomenon, it is crucial to go beyond mean-fieldtheory (or, equivalently, beyond the leading order term in a $1/N$ expansion).Interestingly, on the lattice, the chiral Gross-Neveu model appears at aLandau-forbidden second order phase transition separating two distinct andunrelated symmetry-breaking orders. We point out the crucial role of twodifferent 't Hooft anomalies or Lieb-Schultz-Mattis obstructions for thisLandau-forbidden phase transition to occur.

The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition