We carry out large-scale, sign-problem-free determinant quantum Monte Carlo simulations of the square lattice $\mathrm{SU}(N)$-symmetric two-channel Kondo lattice model at half-filling. We map out the zero-temperature phase diagram for $N=2$, 4, 6, and 8, as a function of the Kondo coupling strength. In the weak-coupling regime, we observe antiferromagnetic order of the localized moments. Remarkably, for $N\ge 6$, sufficiently strong Kondo coupling induces spontaneous channel symmetry breaking, forming a stripe dimerization pattern with a wave vector $\mathit{k}=(\pi ,0)$ alternating between channels. These findings are supported by a complementary large-$N$ saddle point analysis, which identifies the striped hybridization pattern as the energetically preferred configuration. The spatial symmetry breaking results in an anisotropic Fermi surface reconstruction.

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• Quantum phase transitions
• Heavy-fermion systems
• Strongly correlated systems
• Kondo lattice model
• Large-N expansion in field theory
• Quantum Monte Carlo
• SU(N) symmetries