Ordering of water molecules confined in beryl: A theoretical study

In agreement with recent NMR experiments on beryl crystals containing confined water molecules, we developed an improved model for studying the interactions among the water molecules' dipole moments. The model is based on a local crystal potential with a dihexagonal symmetry for the rotations of the water dipole moments, leading to their deflection from the $ab$ hexagonal crystallographic plane. This shape of the potential implies nontrivial consequences concerning the dipole ordering, which are linked to the non-zero projection of the dipole moment along the hexagonal $c$ axis. We used a variational mean-field approximation, Monte Carlo simulations, and quantum tunneling to reveal a tendency toward three types of equilibrium-ordered states. These states involve a purely planar dipole order with an antiparallel arrangement in the adjacent planes, a configuration with deflected dipole moments ordered in antiparallel directions, and a helical structure of the dipoles twisting along the $c$ axis.Comment: RevTeX4-2, 16 figure

Critical behavior in self-consistent conserving approximations of correlated electrons

We disclose a serious deficiency of the self-consistent conserving approximations of strongly correlated electron systems. There are two vertices, the divergence of each indicates a phase instability. We show that they generically display incomplete and mutually inconsistent critical behavior at different critical points. The dynamical vertex from the Schwinger-Dyson equation cannot be continued beyond its singularity since it does not obey the Ward identity and results in non-conserving response functions. The divergence in the conserving vertex, obeying the conservation laws, does not invoke a critical behavior of the spectral function and the specific heat. We demonstrate this ubiquitous ambiguity on an example of the single-impurity Anderson model. The dynamical vertex leads to strong coupling asymptotics with a logarithmic Kondo scale, while the conserving vertex results in magnetic instability of a spin-symmetric solution at a finite interaction strength.Comment: 5 pages, 2 figures, 1 Supplemental Materia

Kondo behavior in the asymmetric Anderson model: Analytic approach

The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical regions of singularities in the two-particle vertex. The scale vanishing at the critical point defines the Kondo temperature at which the electron-hole correlation function saturates. We show that the Kondo temperature exists at any filling of the impurity level. A quasiparticle resonance peak in the spectral function, however, forms only in almost electron-hole symmetric situations. We relate the Kondo temperature with the width of the resonance peak. Finally we discuss the existence of satellite Hubbard bands in the spectral function.Comment: REVTeX4, 11 pages, 5 EPS figure