Symmetry-protected Bose-Einstein condensation of interacting hardcore Bosons

TL;DR

This paper presents a new mechanism for stabilizing a one-dimensional Bose-Einstein condensate of hardcore bosons using symmetry protection, demonstrated through an exact solution on a wheel geometry and numerical robustness checks.

Contribution

It introduces a symmetry-protected mechanism for Bose-Einstein condensation in 1D systems and provides an exact solution approach applicable to related geometries.

Findings

Demonstrated robustness of condensate with added interactions

Identified energy scale for symmetry protection

Proposed applications for finite-momentum condensates

Abstract

We introduce a mechanism stabilizing a one-dimensional quantum many-body phase, characterized by a certain wave vector $k_0$, from a $k_0$-modulated coupling to a center site, via the protection of an emergent $\mathbb Z_2$ symmetry. We illustrate this mechanism by constructing the solution of the full quantum many-body problem of hardcore bosons on a wheel geometry, which are known to form a Bose-Einstein condensate. The robustness of the condensate is shown numerically by adding nearest-neighbor interactions to the wheel Hamiltonian. We identify the energy scale that controls the protection of the emergent $\mathbb Z_2$ symmetry. We discuss further applications such as geometrically inducing finite-momentum condensates. Since our solution strategy is based on a generic mapping from a wheel geometry to a projected ladder, our analysis can be applied to various related problems with extensively scaling coordination numbers.