Rigidity of interfaces in the Falicov-Kimball model

TL;DR

This paper investigates the rigidity of interfaces in the three-dimensional Falicov-Kimball model, revealing that certain interfaces are stable due to quantum effects, contrasting with classical expectations from the Ising model.

Contribution

It demonstrates the stability of the 111 interface in the Falicov-Kimball model at low temperatures, highlighting the role of Fermi statistics in ground state selection.

Findings

The 100 interface is rigid, similar to the Ising model.

The 111 interface is stable despite being unstable in the Ising model.

Fermi statistics induce ground state selection, leading to interface stability.

Abstract

We analyze the thermodynamic properties of interfaces in the three-dimensional Falicov Kimball model, which can be viewed as a primitive quantum lattice model of crystalline matter. In the strong coupling limit, the ionic subsystem of this model is governed by the Hamiltonian of an effective classical spin model whose leading part is the Ising Hamiltonian. We prove that the 100 interface in this model, at half-filling, is rigid, as in the three-dimensional Ising model. However, despite the above similarities with the Ising model, the thermodynamic properties of its 111 interface are very different. We prove that even though this interface is expected to be unstable for the Ising model, it is stable for the Falicov Kimball model at sufficiently low temperatures. This rigidity results from a phenomenon of "ground state selection" and is a consequence of the Fermi statistics of the electrons in the model.