Nematic Phase Transitions in 1D Flat Band Condensates

Abstract

We investigate the ground-state properties of one-dimensional Gross-Pitaevskii flat-band lattices which are parametrized through their compact localized state (CLS) amplitudes. We uncover a CLS geometry-driven phase transition into a macroscopically degenerate nematic state with broken time-reversal symmetry. The transition is marked by the appearance of constant-density flat-band states and a vanishing sound velocity. We demonstrate that even infinitesimal onsite interactions can destabilize a $k=0$ plane wave condensate, driving the system into a nematic manifold, which persists for any interaction strength. For the particular choice of constant density CLSs which can tile the lattice, we identify additional families of continuously degenerate ground states characterized by vanishing phase stiffness. Utilizing Bogoliubov-de Gennes excitations and parallel tempering, we show that these tiling phases are thermally selected at low temperatures via an order-by-disorder mechanism. We exemplify our findings for different classes of flat bands. Our findings also reveal that the sound velocity in flat-band condensates is a sensitive probe of the underlying nematic phase transitions.