Liquid-liquid transition in a Bose fluid near collapse

Discovering novel emergent behavior in quantum many-body systems is a main objective of contemporary research. In this paper, we explore the effects on phases and phase transitions of the proximity to a Ruelle-Fisher instability, marking the transition to a collapsed state. To accomplish this, we study by quantum Monte Carlo simulations a two-dimensional system of soft-core bosons interacting through an isotropic finite-ranged attraction, with a parameter $\eta$ describing its strength. If $\eta$ exceeds a characteristic value $\eta_c$, the thermodynamic limit is lost, as the system becomes unstable against collapse. We investigate the phase diagram of the model for $\eta\lesssim\eta_c$, finding -- in addition to a liquid-vapor transition -- a first-order transition between two liquid phases. Upon cooling, the high-density liquid turns superfluid, possibly above the vapor-liquid-liquid triple temperature. As $\eta$ approaches $\eta_c$, the stability region of the high-density liquid is shifted to increasingly higher densities, a behavior at variance with distinguishable quantum or classical particles. Finally, for $\eta$ larger than $\eta_c$ our simulations yield evidence of collapse of the low-temperature fluid for any density; the collapsed system forms a circular cluster whose radius is insensitive to the number of particles.