Symmetry breaking in self-consistent models: Lessons from an exactly solvable many-fermion model

TL;DR

This paper introduces an exactly solvable many-fermion model exhibiting a quantum phase transition and symmetry breaking, providing insights into mean-field approximations and phase transitions in fermionic systems.

Contribution

It presents a novel exactly solvable model that demonstrates symmetry breaking and phase transitions, serving as a valuable benchmark for self-consistent fermionic theories.

Findings

Model exhibits a second order insulator-metal quantum phase transition

Mean field ground state shows a liquid-solid transition

Model provides lessons on symmetry breaking in fermionic systems

Abstract

This work presents a many-fermion Hamiltonian with the following properties: 1) is exactly solvable, 2) has a second order insulator-metal quantum phase transition, 3) has a well defined mean field approximation and 4) its mean-field ground state displays a liquid-solid transition. The phenomenon of symmetry breaking in fermionic self-consistent models is discussed in the light of these remarkable properties of the many-body model.