Spontaneous symmetry breaking on interacting Euclidean and hyperbolic non-Hermitian fermionic systems

Spontaneous symmetry breaking plays an important role in the dynamic mass generation of particles in the Standard model, known as the Anderson-Higgs mechanism. It can take place via a quantum phase transition at a finite strength of an appropriate interaction or even for infinitesimally strong interactions depending on the scaling of the density of states. In this talk, I will show that this concept is applicable even for non-Hermitian (NH) materials from extensive bipartite lattice-based self-consistent Hartree-Fock numerical analyses of the nearest-neighbor Coulomb repulsion model for spinless (taken only for simplicity) fermions. First, I will promote a general principle of constructing non-Hermitian operators on any bipartite lattice, embedded on flat Euclidean or curved hyperbolic space, that over an extended parameter regime is guaranteed to feature a real eigenvalue spectrum. Next, I will show that in such a parameter regime, the non-Hermitian parameter enhances the tendency of a charge-density-wave (CDW) ordering by spontaneously breaking the sublattice inversion symmetry, making it more prominent at weaker interactions in comparison to its counterpart in Hermitian systems. Nucleation of the CDW ordering dynamically develops mass gap for NH fermionic excitations. I will establish that this is a generic and robust phenomenon, which is operative on any flat Euclidean and curved hyperbolic bipartite lattice, supporting either vanishing (NH Dirac liquid), constant (NH Fermi liquid), or diverging (NH flat band) density of states. If time permits, I will also discuss the role of external magnetic fields on the dynamic mass generation in NH Dirac liquids.