Inversion symmetry breaking and criticality in free fermionic lattices

Zoltan Kadar

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arXiv · 1607.08594

Inversion symmetry breaking and criticality in free fermionic lattices

Zoltan Kadar

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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.

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Zoltan Kadar. 2016-07-28. Inversion symmetry breaking and criticality in free fermionic lattices. https://arxiv.org/abs/1607.08594

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