Remanent Magnetization: Signature of Many-Body Localization in Quantum Antiferromagnets

We study the remanent magnetization in antiferromagnetic, many-body localized quantum spin chains, initialized in a fully magnetized state. Its long time limit is an order parameter for the localization transition, which is readily accessible by standard experimental probes in magnets. We analytically calculate its value in the strong-disorder regime exploiting the explicit construction of quasilocal conserved quantities of the localized phase. We discuss analogies in cold atomic systems.

Figure 1

Relaxation of the total magnetization from a fully polarized initial state. The black curve is the stationary value $L^{-1}\sum _j{\widehat{m}}_j$: it vanishes (possibly discontinuously [35, 36]) at the critical point separating the many-body localized and delocalized phases (red point). It is nonanalytic for $J_x/h\ll 1$, cf. Eq. (13).

Figure 2

Dependence of the remanent density imbalance on the hopping strength $J$ for a chain of noninteracting fermions ($L=100$, $5\times 10^3$ realizations). The continuous red line is the analytical estimate, Eq. (13), with $J_x=J$, $J_z=0$. The blue dashed line is a power law fit $a+c(J/h{)}^{-2}$, with $a=0.003$, $c=0.101$.