Symmetry-protected Bose-Einstein condensation of interacting hardcore Bosons

The past two decades have seen the raise of practical applications of exotic quantum many-body phases. Proving their potential to overcome classical solution strategies to relevant problem settings, one of the main obstacles nowadays is to stabilize these highly fragile quantum states against perturbations. Here, we demonstrate the stabilization of a one-dimensional quantum many-body phase, characterized by a certain wave vector k, from a k-modulated coupling to a center site via the protection of an emergent Z₂ symmetry. We illustrate this mechanism by constructing the solution to the full quantum many-body problem of hardcore bosons on a wheel geometry, which is known to form a BEC. The crucial step is to map the wheel to a projected ladder geometry, where the protection of the Z₂ symmetry is manifested by the choice of a particular k mode spanning the projected subspace on one leg of the ladder. The robustness of the BEC is shown numerically by adding local interactions to the wheel Hamiltonian and we identify the energy scale that controls the protection of the emergent Z₂ symmetry. Since the protection is generated by gapping out an independently selectable k mode from the single-particle spectrum, our findings can be generalized, for instance to create a k≠0 BEC.