Many-Body Localization in Dipolar Systems

Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the presence of power-law interactions and supplement our analytic treatment with numerical evidence of localized states in one dimension. We propose and analyze several experimental systems that can be used to observe and probe such states, including ultracold polar molecules and solid-state magnetic spin impurities.

Figure 1

(a) Schematic of four-spin resonance structure. Each pair of (red) spins at separation $R_1$ forms a pseudospin (blue) with the level structure shown below. (b) A pseudospin at the origin resonates with another pseudospin in a shell $R_2<r<2R_2$.

Figure 2

Finite-size scaling of the long-time dynamic polarization for Eq. (1) in $d=1$ (with units $t=1$, $V=2$) with (a) $\alpha =\beta =1$, (b) $\alpha =\beta =3/2$, (c) $\alpha =\beta =2$, and (d) $\alpha =\beta =3$. The lack of flow reversal in (a) suggests delocalization at all disorders. The sharpening of the crossover as a function of increasing system size in (d) suggests the existence of a phase transition at approximately $W_c\approx 10$ into an MBL phase. The flow at intermediate power laws (b) is inconclusive.

Figure 3

(a) Schematic of the one-dimensional tube geometry with strong confinement in the $\widehat{y}$ and $\widehat{z}$ directions and hopping in the $\widehat{x}$ direction. (b) Dipolar molecules in each 1D tube are subject to an optical speckle pattern that generates an effective random on-site chemical potential for the hopping molecules. (c) Schematic of the dipolar “spin” hopping model. Molecules pinned with dilution in the deep optical lattice may exchange rotational excitations. (d) Effective rotational level structure of a polar molecule, with $|\uparrow ⟩=|1,1⟩$, $|\downarrow ⟩=|0,0⟩$ shown for the $\alpha =\beta =3$ rotor model. (e) Level structure of two polar molecules for the $\alpha =6$ rotor model, wherein hopping is mediated by a second-order dipolar process.

Figure 4

Exact diagonalization study of Eq. (1) with nearest-neighbor hopping ($\alpha \to \infty$) and dipolar interactions ($\beta =3$). Random fields are drawn from a uniform distribution of width $W$. (a) Finite-size scaling of the long-time dynamic polarization. The finite-size flow suggests a delocalization phase transition at $W_c\approx 1.4t$. (b) MBL phase boundaries determined by finite-size flow for $V/t=1,2,4$.