Anisotropic c−f Hybridization in the Ferromagnetic Quantum Critical Metal CeRh6Ge4

Magnetic order and crystalline electric field excitations of the quantum critical heavy-fermion ferromagnet CeRh6Ge4

“…To account for this behavior in light of the previously reported prohibition of FM QCPs in itinerant systems, it was proposed that CeRh 6 Ge 4 exhibits local quantum criticality, where the requisite entanglement of the local moments is generated by their xy anisotropy [17]. Moreover, in such local FM quantum critical models, quasi-1D exchange interactions appear to be vital for avoiding a first-order transition [17,19], which is in accordance with angle-resolved photoemission spectroscopy (ARPES) measurements revealing evidence for highly anisotropic c − f coupling in CeRh 6 Ge 4 , from the observation of strong anisotropy in the hybridization [20]. Alternatively, it was proposed that the pressure-induced first-order transition is avoided by the soft modes, which prevent FM quantum criticality, becoming massive due to the antisymmetric spin-orbit coupling arising from the broken inversion symmetry in the crystal lattice (space group P 6m2) [21].…”

“…This could potentially reconcile there being significant Kondo screening processes which reduce the ordered moment, with the conclusion of localized 4 f electrons inferred from quantum oscillation measurements [28]. These results suggest that the anisotropy of the CEF orbitals is an important factor in the observed anisotropic hybridization [20], and such anisotropic c − f coupling may also give rise to quasi-1D magnetic exchange interactions, which have been proposed to avoid the first-order transition ubiquitous to isotropic systems [17,19]. As such, materials with similarly anisotropic ground-state orbitals could be good candidates for searching for additional quantum critical ferromagnets.…”

“…The angular distributions of the CEF wave functions are also displayed. Notably, both the ground state and first excited doublet at 5.8 meV primarily have electron density out of the basal plane, which may explain the strongly anisotropic hybridization revealed by ARPES, with significantly stronger hybridization along the c axis [20]. Moreover, the low-lying first excited doublet appears to hybridize much more strongly with the conduction electrons, which may be a consequence of greater overlap with the out-of-plane Rh(2) and Ge(2) atoms, while ground-state charge density is orientated toward the neighboring Ce atoms [Fig.…”

Uncovering the peculiar 4f electrons in heavy fermions

“…Quantum oscillation (QO) experiments below T c at ambient pressure revealed oscillation frequencies in good agreement with localized 4f calculations [8]. Meanwhile, ARPES measurements uncovered dispersive 4f bands near E F well above T c [9]. The hybridization strength was found to be quite anisotropic in momentum space due to the Ce chains, likely an important ingredient for the FM quantum criticality.…”

Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations

“…Here we show that previously difficult EE measurements can be greatly optimized and improved via the nonequilibrium increment method, and in this way, one can investigate the scaling behavior of EE in many (2 + 1)d quantum many-body systems with unprecedentedly large system sizes, controlled errorbars and minimal computational costs. Starting from the three representative cases shown here, one can foresee the implementation and measurement of EE via the Qiu Ku algorithm for other topological ordered phases and phase transitions, interacting fermionic systems such as the Gross-Neveu QCPs with critical Dirac fermions [83], the deconfined QED 3 problems of gauge fields coupled to fermion matter fields [84][85][86] and the more complicated situations of non-Fermi-liquid and quantum critical metals [87][88][89][90][91][92][93][94][95] and hopefully make further suggestions to the on-going experimental search for these strongly entangled quantum matter.…”