Abstract
Using mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling. The symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it possible to study the behavior of an electron liquid in the Kondo lattice. We have shown that, due to hybridization (through an effective field due to localized electrons) of electrons with different spins and momenta mathbf{k} and mathbf{k} +overrightarrow{pi }, the gap in the electron spectrum opens at half filling. Such hybridization breaks the conservation of the total magnetic momentum of electrons, the spontaneous symmetry is broken. The state of electron liquid is characterized by a large Fermi surface. A gap in the spectrum is calculated depending on the magnitude of the on-site Coulomb repulsion and value of s–d hybridization for the chain, as well as for square and cubic lattices. Anomalous behavior of the heat capacity at low temperatures in the gapped state, which is realized in the symmetric Anderson lattice, was also found.
Highlights
C T calculated for cubic lattice at UThe nontrivial solution for , shown, corresponds to stable insulator state at U = 2 , the gapped state at U = 1 , is unstable
Using mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling
Using mean field approximation we have considered the solution of the symmetric Anderson lattice at half-filling for different dimensions of the lattice
Summary
The nontrivial solution for , shown, corresponds to stable insulator state at U = 2 , the gapped state at U = 1 , is unstable. Taking into account the spectrum of quasi particle excitations (2) in the action (6), we determine the low temperature behavior of the specific heat (its electronic part) for 3D system (cubic lattice). (see Fig. 6a) and v = 0.5 , = 0.07 , = 0.0279 (see Fig.6b) Note that for these parameters, the gaps in the electron spectrum differ by an order of magnitude. The temperature range and the minimum value depend on the value of the gap
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