Two-Stage Melting in Systems of Strongly Interacting Rydberg Atoms

We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil’s staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low-energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transition and the ground state becomes paramagnetic.

Figure 1

Ground state phase diagram: We find commensurate solids with filling $f=p/q$ describing a complete devil’s staircase for $\Omega =0$. The lobes with $p>1$ are not visible within this scale. For increasing Rabi frequency $\Omega$, a quantum phase transition takes place into a gapless floating solid (FS) with algebraic correlations for the solid structure and in general incommensurate density, and eventually a second melting transition occurs into a gapped paramagnet (PM). This second transition line satisfies $\Delta \sim {\Omega }^{12/13}$.

Figure 2

Processes in second order perturbation theory. (a) Virtual annihilation of a Rydberg excitation. (b) Virtual creation of a Rydberg excitation. (c) Hopping of a crystal defect.

Figure 3

Decay of the spin correlations from Monte-Carlo simulations (crosses) according to $c/\sqrt{\ln j/b^{\prime }}$ (solid line) as predicted by Luttinger liquid theory ($q=6$, $n=0.25$). The crossover to the algebraic decay takes place at much larger distances $|i-j|\sim {10}^9$. The inset shows the oscillations of the correlation function.