Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model

We investigate the quantum phases of hard-core bosonic atoms in an extended Hubbard model where particles interact via soft-shoulder potentials in one dimension. Using a combination of field-theoretical methods and strong-coupling perturbation theory, we demonstrate that the low-energy phase can be a conformal cluster Luttinger liquid (CLL) phase with central charge $c=1$, where the microscopic degrees of freedom correspond to mesoscopic ensembles of particles. Using numerical density-matrix-renormalization-group methods, we demonstrate that the CLL phase, first predicted in [Phys. Rev. Lett. 111, 165302 (2013)], is separated from a conventional Tomonaga-Luttinger liquid by an exotic critical point with central charge $c=3/2$. The latter is expression of an emergent conformal supersymmetry, which is not present in the original Hamiltonian. We discuss the observability of the CLL phase in realistic experimental settings with weakly-dressed Rydberg atoms confined to optical lattices. Using quantum Monte-Carlo simulations, we show that the typical features of CLLs are stable up to comparatively high temperatures. Using exact diagonalizations and quantum trajectory methods, we provide a protocol for adiabatic state preparation as well as quantitative estimates on the effects of particle losses.

Cavity Optomechanics of Levitated Nano-Dumbbells: Non-Equilibrium Phases and Self-Assembly

Levitated nanospheres in optical cavities open a novel route to study many-body systems out of solution and highly isolated from the environment. We show that properly tuned optical parameters allow for the study of the non-equilibrium dynamics of composite nano-particles with non-isotropic optical friction. We find friction induced ordering and nematic transitions with non-equilibrium analogs to liquid crystal phases for ensembles of dimers.