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In heavy-fermion systems, the competition between the local Kondo physics andintersite magnetic fluctuations results in unconventional quantum criticalphenomena which are frequently addressed within the Kondo lattice model (KLM).Here we study this interplay in the SU($N$) symmetric generalization of thetwo-dimensional half-filled KLM by quantum Monte Carlo simulations with $N$ upto 8. While the long-range antiferromagnetic (AF) order in SU($N$) quantum spinsystems typically gives way to spin-singlet ground states with spontaneouslybroken lattice symmetry, we find that the SU($N$) KLM is unique in that foreach finite $N$ its ground-state phase diagram hosts only two phases -- AForder and the Kondo-screened phase. The absence of any intermediate phasebetween the $N=2$ and large-$N$ cases establishes adiabatic correspondencebetween both limits and confirms that the large-$N$ theory is a correct saddlepoint of the KLM fermionic path integral and a good starting point to includequantum fluctuations. In addition, we determine the evolution of thesingle-particle gap, quasiparticle residue of the doped hole at momentum$(\pi,\pi)$, and spin gap across the magnetic order-disorder transition. Ourresults indicate that increasing $N$ modifies the behavior of the coherencetemperature: while it evolves smoothly across the magnetic transition at $N=2$it develops an abrupt jump -- of up to an order of magnitude -- at larger butfinite $N$. We discuss the magnetic order-disorder transition from aquantum-field-theoretic perspective and comment on implications of our findingsfor the interpretation of experiments on quantum critical heavy-fermioncompounds.

Phase diagram and dynamics of the SU($\boldsymbol N$) symmetric Kondo lattice model