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Motivated by the recent discovery of ferromagnetic quantum criticality in theheavy fermion compound CeRh$_6$Ge$_4$, we develop a numerical algorithm ofinfinite projected entangled pair states for the anisotropic ferromagneticKondo-Heisenberg model in two dimensions and study the ferromagnetic quantumphase transitions with varying magnetic and hopping anisotropy. Ourcalculations reveal a continuous ferromagnetic quantum phase transition in thelarge anisotropic region and first-order quantum phase transitions for smalleranisotropy. Our results highlight the importance of magnetic anisotropy onferromagnetic quantum criticality in Kondo lattice systems and provide apossible explanation for the experimental observation in CeRh$_6$Ge$_4$ with aquasi-one-dimensional magnetic structure. Our work opens the avenue for futurestudies of the rich Kondo lattice physics using state-of-the-art tensor networkapproaches.

Continuous ferromagnetic quantum phase transition on an anisotropic Kondo lattice