Inversion symmetry breaking and criticality in free fermionic lattices

TL;DR

This paper establishes a link between inversion symmetry breaking and criticality in free fermionic lattice models, showing that symmetry breaking implies long-range correlations and gapless spectra, with implications for the validity of Hartree-Fock approximations.

Contribution

It introduces invariants under translation-invariant free fermion quenches to connect symmetry breaking with criticality, providing new insights into fermionic lattice models.

Findings

Inversion symmetry breaking implies criticality in spinless fermion models.

Symmetry breaking in spin models is indicated by spin-averaged covariance matrix asymmetry.

Identifies models where Hartree-Fock approximation fails due to symmetry considerations.

Abstract

We describe the connection between inversion symmetry breaking and criticality in free fermionic lattice models. It is shown that for translation-invariant spinless fermions, the breaking of this symmetry in the ground state implies criticality, i.e., the existence of long-range correlations and the vanishing of the spectral gap; while for models with spin, only the asymmetry of the spin-averaged covariance matrix implies a similar conclusion. Our results are proved by introducing invariants under global translation-invariant free fermion quenches. Using this result, we identify a set of models where the generalized Hartree-Fock approximation must break down.