Quantum phase transition in the Kondo lattice model

Motivated by the recent discovery of ferromagnetic quantum criticality in the heavy fermion compound ${\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}$ , we develop a numerical algorithm of infinite projected entangled pair states for the anisotropic ferromagnetic Kondo-Heisenberg model in two dimensions and study the ferromagnetic quantum phase transitions with varying magnetic and hopping anisotropy. Our calculations reveal a continuous ferromagnetic quantum phase transition in the large anisotropic region and first-order quantum phase transitions for smaller anisotropy. Our results highlight the importance of magnetic anisotropy on ferromagnetic quantum criticality in Kondo lattice systems and provide a possible explanation for the experimental observation in ${\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}$ with a quasi-one-dimensional magnetic structure. Our work opens the avenue for future studies of the rich Kondo lattice physics using state-of-the-art tensor network approaches.Motivated by the recent discovery of ferromagnetic quantum criticality in the heavy fermion compound ${\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}$, we develop a numerical algorithm of infinite projected entangled pair states for the anisotropic ferromagnetic Kondo-Heisenberg model in two dimensions and study the ferromagnetic quantum phase transitions with varying magnetic and hopping anisotropy. Our calculations reveal a continuous ferromagnetic quantum phase transition in the large anisotropic region and first-order quantum phase transitions for smaller anisotropy. Our results highlight the importance of magnetic anisotropy on ferromagnetic quantum criticality in Kondo lattice systems and provide a possible explanation for the experimental observation in ${\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}$ with a quasi-one-dimensional magnetic structure. Our work opens the avenue for future studies of the rich Kondo lattice physics using state-of-the-art tensor network approaches.

arXiv:2203.15475Physical review. B./Physical review. BAug 5, 20228 citations

Quantum Phase Transition in Multi-channel Kondo Systems

Zubair Iftikhar

Springer thesesJan 1, 20181 citation

Cavity control of quantum phase transitions in a two-dimensional Kondo lattice

Jun Mochida, Atac Imamoglu, Yuto Ashida

Cavity quantum electrodynamics offers a route to control quantum phases by using vacuum fluctuations of confined electromagnetic fields. In particular, planar cavities based on polar van der Waals materials can generate strongly confined modes and are promising for controlling two-dimensional correlated materials. Recently, moiré materials have become central platforms for studying two-dimensional heavy-fermion systems and their quantum phase transitions. Kondo lattices provide a prototypical model for studying quantum phase boundaries, driven by competition between Kondo screening and the ordering of local magnetic moments. We show that a cavity-induced interaction can shift the quantum phase transitions between a heavy-fermion phase and an antiferromagnetic phase in a two-dimensional Kondo lattice through a momentum-dependent self-energy of the conduction bands. For the longitudinal projected field motivated by h-BN hyperbolic phonon polaritons, the self-energy favors Kondo hybridization and expands the heavy-fermion region. Transverse and circular in-plane model structures give distinct effects, with the transverse case relatively favoring the magnetically ordered phase and the circular case lying between the longitudinal and transverse cases. These results indicate that electromagnetic vacuum fluctuations can effectively modify the control parameters of strongly correlated two-dimensional Kondo materials.Cavity quantum electrodynamics offers a route to control quantum phases by using vacuum fluctuations of confined electromagnetic fields. In particular, planar cavities based on polar van der Waals materials can generate strongly confined modes and are promising for controlling two-dimensional correlated materials. Recently, moiré materials have become central platforms for studying two-dimensional heavy-fermion systems and their quantum phase transitions. Kondo lattices provide a prototypical model for studying quantum phase boundaries, driven by competition between Kondo screening and the ordering of local magnetic moments. We show that a cavity-induced interaction can shift the quantum phase transitions between a heavy-fermion phase and an antiferromagnetic phase in a two-dimensional Kondo lattice through a momentum-dependent self-energy of the conduction bands. For the longitudinal projected field motivated by h-BN hyperbolic phonon polaritons, the self-energy favors Kondo hybridization and expands the heavy-fermion region. Transverse and circular in-plane model structures give distinct effects, with the transverse case relatively favoring the magnetically ordered phase and the circular case lying between the longitudinal and transverse cases. These results indicate that electromagnetic vacuum fluctuations can effectively modify the control parameters of strongly correlated two-dimensional Kondo materials.

cond-mat.str-elCross-listedarXiv:2608.03714Aug 5, 2026

Phase diagram of the 1D Kondo lattice model

Ian P. McCulloch, M. Gulácsi, S. Caprara +2 more

arXiv:cond-mat/9908414Journal of Low Temperature PhysicsNov 1, 199921 citations

Motivated by the recent discovery of ferromagnetic quantum criticality in the heavy fermion compound

{\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}

, we develop a numerical algorithm of infinite projected entangled pair states for the anisotropic ferromagnetic Kondo-Heisenberg model in two dimensions and study the ferromagnetic quantum phase transitions with varying magnetic and hopping anisotropy. Our calculations reveal a continuous ferromagnetic quantum phase transition in the large anisotropic region and first-order quantum phase transitions for smaller anisotropy. Our results highlight the importance of magnetic anisotropy on ferromagnetic quantum criticality in Kondo lattice systems and provide a possible explanation for the experimental observation in

{\mathrm{CeRh}}_{6}{\mathrm{Ge}}_{4}

with a quasi-one-dimensional magnetic structure. Our work opens the avenue for future studies of the rich Kondo lattice physics using state-of-the-art tensor network approaches.