Topological multicriticality of spin-orbit coupled electrons in one dimension

A central tenet in the theory of quantum phase transitions (QPTs) is that a nonanalyticity in the ground state energy in the thermodynamic limit implies a QPT. Here we report on a finding that challenges this assertion. As a case study we take the phase diagram of a one-dimensional band insulator with spin-orbit coupled electrons with trivial and topological gapped phases separated by intersecting critical surfaces. The intersections define multicritical lines across which the ground state energy becomes nonanalytical, but with no phase transition taking place. We propose a simple picture for how multicriticality gives rise to this unexpected phenomenon.