Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
Phys. Rev. B 113, 155152 – Published 27 April, 2026
DOI: https://doi.org/10.1103/3l8x-ffmn
Abstract
Depending on the lattice geometry, the prototypical nearest-neighbor (NN) tight-binding model for free fermions gives rise to particle-hole symmetric emergent Dirac liquids, Fermi liquids, and (quasi)flat bands near half filling or zero energy on (bipartite) Euclidean and hyperbolic lattices, respectively, embedded on flat and negatively curved spaces. Such noninteracting electronic fluids are characterized by a vanishing, a finite, and a diverging density of states near the half-filling, respectively. Here, we outline a general principle of realizing non-Hermitian (NH) generalizations of these scenarios in which the resulting NH operator features an all-real eigenvalue spectrum over an extended NH parameter regime where all the single-particle states remain sharp and filling factor is well defined. Most importantly, such a construction reduces the bandwidth of noninteracting systems without altering the characteristic scaling of the density of states close to the zero energy, thereby triggering the ordering propensity toward the nucleation of a family of spontaneous symmetry-breaking quantum phases, named commuting-class masses, at weaker interactions. We name this phenomenon ‘‘non-Hermitian catalysis of spontaneous symmetry breaking’’ that hinges on a robust and universal algebraic criterion, ultimately liberating this mechanism from the burden of the underlying lattice specification as well as the dimensionality of the system. We establish the NH catalysis of commuting-class masses from the numerical self-consistent solutions of the charge-density-wave and spin-density-wave orders at weaker (in comparison to the counterparts in conventional or Hermitian systems) NN Coulomb and on-site Hubbard repulsions, respectively, obtained by decomposing them in the Hartree channel when combined with the biorthogonal quantum mechanics on NH Euclidean and hyperbolic lattices in which the non-Hermiticity results from an imbalance of the hopping amplitudes between the sites of two sublattices in the opposite directions. These two ordered states correspond to staggered patterns of average electronic density and spin between the NN sites, respectively, and both cause insulation in half-filled systems. We discuss the scaling of the associated mass gaps near the zero energy with the non-Hermitian parameter, showing excellent agreement with analytical predictions, and also address the finite-size scaling of the order parameters specifically on hyperbolic lattices with open boundary conditions. We conclude with an outline of possible experimental platforms to test our concrete theoretical predictions.
