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 the Kondo lattice model

Ki‐Seok Kim, Mun Dae Kim

Aug 10, 20060 citations

Ordering and criticality in an underscreened Kondo chain

Wing-Ho Ko, Hong‐Chen Jiang, Jeffrey G. Rau +1 more

Motivated by the nickel valence controversy in the perovskite nickelate $R$ NiO ${}_{3}$ , we consider a one-dimensional underscreened Kondo chain consisting of alternating spin-1 (``nickel'') and electron (``oxygen'') sites, which in addition to the usual electron hopping and spin-spin interaction between the $S=1$ spin and the electron also contains a spin-mediated electron hopping term. Using the density-matrix renormalization group (DMRG), we obtained the zero-temperature phase diagram of the model, as well as various correlation functions in each phase. Importantly, for a certain range of parameters the model exhibits a quasi-long-range spiral (QS) order. To understand the DMRG results, we construct a mean-field theory based on a Schwinger fermion decomposition of the $S=1$ spins, from which we argue that the QS phase corresponds to a phase in proximity to the spin Bose metal state proposed by Sheng, Motrunich, and Fisher [Phys. Rev. B 79, 205112 (2009)]. Notably, we find no evidence for a phase with the symmetry of ``nickel''-centered charge order, which has been argued to arise due to site-selective Kondo screening of half the $S=1$ spins, and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions, not present in this model.Motivated by the nickel valence controversy in the perovskite nickelate $R$NiO${}_{3}$, we consider a one-dimensional underscreened Kondo chain consisting of alternating spin-1 (``nickel'') and electron (``oxygen'') sites, which in addition to the usual electron hopping and spin-spin interaction between the $S=1$ spin and the electron also contains a spin-mediated electron hopping term. Using the density-matrix renormalization group (DMRG), we obtained the zero-temperature phase diagram of the model, as well as various correlation functions in each phase. Importantly, for a certain range of parameters the model exhibits a quasi-long-range spiral (QS) order. To understand the DMRG results, we construct a mean-field theory based on a Schwinger fermion decomposition of the $S=1$ spins, from which we argue that the QS phase corresponds to a phase in proximity to the spin Bose metal state proposed by Sheng, Motrunich, and Fisher [Phys. Rev. B 79, 205112 (2009)]. Notably, we find no evidence for a phase with the symmetry of ``nickel''-centered charge order, which has been argued to arise due to site-selective Kondo screening of half the $S=1$ spins, and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions, not present in this model.

arXiv:1301.3538Physical Review BMay 8, 20133 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.

Motivated by the nickel valence controversy in the perovskite nickelate

R

NiO

{}_{3}

, we consider a one-dimensional underscreened Kondo chain consisting of alternating spin-1 (``nickel'') and electron (``oxygen'') sites, which in addition to the usual electron hopping and spin-spin interaction between the

S=1

spin and the electron also contains a spin-mediated electron hopping term. Using the density-matrix renormalization group (DMRG), we obtained the zero-temperature phase diagram of the model, as well as various correlation functions in each phase. Importantly, for a certain range of parameters the model exhibits a quasi-long-range spiral (QS) order. To understand the DMRG results, we construct a mean-field theory based on a Schwinger fermion decomposition of the

S=1

spins, from which we argue that the QS phase corresponds to a phase in proximity to the spin Bose metal state proposed by Sheng, Motrunich, and Fisher [Phys. Rev. B 79, 205112 (2009)]. Notably, we find no evidence for a phase with the symmetry of ``nickel''-centered charge order, which has been argued to arise due to site-selective Kondo screening of half the

S=1

spins, and suggest that order of this type occurs only due to an additional energy gain from spontaneous lattice distortions, not present in this model.