Analysis of a Model of Condensation for Fermi Systems.

Geo Jose, Kangjun Seo, Bruno Uchoa

We study a two-band dispersive SYK model in $1+1$ dimension. We suggest a model that describes a semimetal with quadratic dispersion at half-filling. We compute the Green's function at the saddle point using a combination of analytical and numerical methods. Employing a scaling symmetry of the Schwinger Dyson equations that becomes transparent in the strongly dispersive limit, we show that the exact solution of the problem yields a distinct type of non-Fermi liquid with sublinear $\rho\propto T^{2/5}$ temperature dependence of the resistivity. A scaling analysis indicates that this state corresponds to the fixed point of the dispersive SYK model for a quadratic band touching semimetal. We examine the formation of indirect exciton condensation in a bilayer system constructed from the above model. We find that the condensation temperature scales as a fast power-law $T_{c}\propto g^{5}$, with $g$ the strength of the repulsive coupling between the layers.

M. Ya. Amusia, Konstantin G. Popov, Vasily R. Shaginyan +1 more

Lan Zhang, Yin Zhong, Hong‐Gang Luo

We investigate a modified Anderson model at the large-N limit, where the Coulomb interaction is replaced by the Sachdev–Ye–Kitaev random interaction. The resistivity of conduction electron ρ c has a minimum value around temperature T*, which is similar to the Kondo system, but the impurity electron’s density of state A d(ω) demonstrates no sharp-peak like the Kondo resonance around the Fermi surface. This provides a counterintuitive example where resistivity minimum exists without Kondo resonance. The impurity electron’s entropy S d and specific heat capacity C v show a crossover from Fermi liquid to a non-Fermi liquid behavior dependent on temperature. The system is a Fermi liquid at T < T*, and becomes a non-Fermi liquid at T > T*, and then becomes a Fermi gas at sufficiently high temperatures T ≫ T*. The non-Fermi liquid at the intermediate-T regime does not occur in the standard Anderson model. We also make a renormalization group analysis, which confirms the crossover from Fermi liquid to the non-Fermi behavior. It is emphasized that the resistivity minimum emerges in our model when the system behaves as a non-Fermi liquid rather than Fermi liquid, which provides an alternative example showing resistivity minimum in condensed matter physics.

M. Beyer

Delle Site, L.

A Thomas-Fermi statistical analysis of Bader's interatomic surface developed in a previous work ( Delle Site L., Phys. Lett. A, 286 ( 2001) 61) is here extended by considering exchange effects and electron density's inhomogeneity at a basic level via the Thomas-Fermi-Dirac-Weizsacker model. The results obtained show interesting connections with Bohmian mechanics and lead to a statistical interpretation of the chemical properties of condensed systems at atomistic level.

Peter Schuck, M. Beyer, GERD RÖPKE +2 more