We investigate the many-body localization (MBL) transition in the quantum Ising model with long-range interactions. Unlike spin chains with short-range interactions, where the MBL transition point remains elusive due to strong finite-size effects and local fluctuations, long-range interactions suppress such fluctuations and enable clearer signatures of critical behavior. Using exact results from a related Bethe lattice localization problem, we estimate the MBL threshold within logarithmic accuracy and find consistency with exact diagonalization. Although the critical disorder diverges in the thermodynamic limit, our results demonstrate that the critical regime can still be probed and highlight the relevance of this model to systems with dipole-dipole, elastic, or indirect exchange interactions.
We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, ${V}_{ij}\ensuremath{\propto}{\left|i\ensuremath{-}j\right|}^{\ensuremath{-}\ensuremath{\alpha}}$, where the exponent of the interaction range $\ensuremath{\alpha}$ can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing $\ensuremath{\alpha}$, the critical exponent experiences a sharp increase at about ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}1.2$ and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$, we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$, the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.
We show that a one-dimensional Hubbard model with all-to-all coupling may exhibit many-body localization in the presence of local disorder. We numerically identify the parameter space where many-body localization occurs using exact diagonalization and finite-size scaling. The time evolution from a random initial state exhibits features consistent with the localization picture. The dynamics can be observed with quantum gases in optical cavities, localization can be revealed through the time-dependent dynamics of the light emitted by the resonator.
We investigate many-body localization in the chain of interacting spins with a transverse power-law interaction, ${J}_{0}/{r}^{\ensuremath{\alpha}}$, and random on-site potentials, ${\ensuremath{\phi}}_{i}\ensuremath{\in}\left(\ensuremath{-}W/2,W/2\right)$, in the long-range limit, $\ensuremath{\alpha}<3/2$, which has been recently examined experimentally on trapped ions. The many-body localization threshold is characterized by the critical disordering,
Wc, which separates localized (
W>Wc) and chaotic (
W<Wc) phases. Using the analysis of the instability of localized states with respect to resonant interactions complemented by numerical finite-size scaling, we show that the critical disordering scales with the number of spins,
N, as ${W}_{c}\ensuremath{\approx}[1.37{J}_{0}/(4/3\ensuremath{-}\ensuremath{\alpha})]{N}^{4/3\ensuremath{-}\ensuremath{\alpha}}lnN$ for $0<\ensuremath{\alpha}\ensuremath{\le}1$, and as ${W}_{c}\ensuremath{\approx}[{J}_{0}/(1\ensuremath{-}2\ensuremath{\alpha}/3)]{N}^{1\ensuremath{-}2\ensuremath{\alpha}/3}{ln}^{2/3}N$ for $1<\ensuremath{\alpha}<3/2$, while the transition width scales as ${\ensuremath{\sigma}}_{W}\ensuremath{\propto}{W}_{c}/N$. We use this result to predict the spin long-term evolution for a very large number of spins (
N=50), inaccessible for exact diagonalization, and to suggest the rescaling of hopping interaction with the system size to attain the localization transition at finite disordering in the thermodynamic limit of infinite number of spins.
We study many-body localization (MBL) for interacting one-dimensional lattice fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing on the role of interaction range. We obtain the MBL quantum phase diagrams by calculating the experimentally relevant inverse participation ratio (IPR) at half-filling using exact diagonalization methods and extrapolating to the infinite system size. For short-range interactions, our results produce in the phase diagram a qualitative symmetry between weak and strong interaction limits. For long-range interactions, no such symmetry exists as the strongly interacting system is always many-body localized, independent of the effective disorder strength, and the system is analogous to a pinned Wigner crystal. We obtain various scaling exponents for the IPR, suggesting conditions for different MBL regimes arising from interaction effects.
We study theoretical transitions between the localized and chaotic many-body regimes in one-dimensional quantum lattice systems with long-range couplings between particles and linear external potential. In terms of established criteria characterizing localization, we construct effective phase diagrams for several types of lattice systems with variable amplitude of the external linear tilt and interaction strength. By means of exact diagonalization and time-dependent variational principle numerical approaches we analyze system dynamics after quenches. Our results reveal that the Stark localization without any artificial source of disorder remains stable upon inclusion of long-range interactions.