Topological Spin Phases of Trapped Rydberg Excitons in ${\mathrm{Cu}}_2\mathrm{O}$

We theoretically study Rydberg excitons in one-dimensional chains of traps in ${\mathrm{Cu}}_2\mathrm{O}$ coupled via the van der Waals interaction. The triplet of optically active $p$-shell states acts as an effective spin 1, and the interactions between the excitons are strongly spin dependent. We predict that the system has the topological Haldane phase with the diluted antiferromagnetic order, long-range string correlations, and finite excitation gap. We also analyze the effect of the trap geometry and interactions anisotropy on the Rydberg exciton spin states and demonstrate that a rich spin phase diagram can be realized showing high tunability of the Rydberg exciton platform.

Figure 1

Schematics of the diluted antiferromagnetic state formed from $p$-shell Rydberg excitons in an array of traps.

Figure 2

Ground and excited state energies in spin chains of different lengths with the periodic boundary conditions. Open symbols correspond to the lowest excited state with the total spin projection $\sum S_j^z=0$, filled symbols correspond to the double-degenerate states with $\sum S_j^z=\pm 1$. Squares indicate results of direct numerical calculation, diamonds correspond to the energies of the variational states Eqs. (3) and (4) with $k=\pi$ and 0, respectively. Dashed lines are the variational results obtained for the infinite system. The inset shows the ground state energy per bond, $E_0/(N\mathcal{E})$, for the finite chain (symbols) and the infinite chain (dashed line).

Figure 3

Spin-spin correlator $(-1{)}^j{C}_{\mathrm{N}é\mathrm{el}}(j)$ and string correlator for ground state of the infinite chain of Rydberg excitons, Eqs. (6) and (7).

Figure 4

Phase diagram of the ground state depending on the trap anisotropy and the spin-spin coupling anisotropy. Insets illustrate the typical spin configurations. The white circle indicates the parameters of Ref. [14] ($D=\delta c_1=0$).