Random Long-range Interactions Research Articles

Many-body localization and enhanced nonergodic subdiffusive regime in the presence of random long-range interactions

We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of random interactions ${V}_{ij}$ decaying as power-law ${V}_{ij}/{({r}_{ij})}^{\ensuremath{\alpha}}$ with distance ${r}_{ij}$. We demonstrate that MBL survives even for $\ensuremath{\alpha}<1$ and is preceded by a broad nonergodic subdiffusive phase. Starting from parameters at which the short-range interacting system shows an infinite temperature MBL phase, turning on random power-law interactions results in many-body mobility edges in the spectrum with a larger fraction of ergodic delocalized states for smaller values of $\ensuremath{\alpha}$. Hence, the critical disorder ${h}_{c}^{r}$, at which ergodic to nonergodic transition takes place, increases with the range of interactions. Time evolution of the density imbalance $I(t)$, which has power-law decay $I(t)\ensuremath{\sim}{t}^{\ensuremath{-}\ensuremath{\gamma}}$ in the intermediate to large time regime, shows that the critical disorder ${h}_{c}^{I}$, above which the system becomes diffusionless (with $\ensuremath{\gamma}\ensuremath{\sim}0$) and transits into the MBL phase, is much larger than ${h}_{c}^{r}$. In between ${h}_{c}^{r}$ and ${h}_{c}^{I}$ there is a broad nonergodic subdiffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions, and a nonzero dynamical exponent $\ensuremath{\gamma}\ensuremath{\ll}1/2$. The system continues to be subdiffusive even on the ergodic side ($h<{h}_{c}^{r}$) of the MBL transition, where the eigenstates near the mobility edges are multifractal. For $h<{h}_{0}<{h}_{c}^{r}$, the system is superdiffusive with $\ensuremath{\gamma}>1/2$. The rich phase diagram obtained here is unique to the random nature of long-range interactions. We explain this in terms of the enhanced correlations among local energies of the effective Anderson model induced by random power-law interactions.

Comment on “Many-body localization in Ising models with random long-range interactions”

This comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power law interactions, $r^{-\alpha}$, relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has been earlier argued [1, 2] that this model obeys the dimensional constraint suggesting the delocalization of all finite temperature states in thermodynamic limit for $\alpha \leq 2d$ in a $d$-dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model in Ref. [3]. To resolve this controversy we reexamine the model of Ref. [3] and demonstrate that the infinite temperature states there obey the dimensional constraint. The earlier developed scaling theory for the critical system size required for delocalization [2] is extended to small exponents $0 \leq \alpha \leq d$. Disagreements between two works are explained by the non-standard selection of investigated states in the ordered phase and misinterpretation of the localization-delocalization transition in Ref. [3].

Many-body localization in Ising models with random long-range interactions

We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, $V_{ij}\propto\left|i-j\right|^{-\alpha}$, where the exponent of the interaction range $\alpha$ 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 $\alpha$, the critical exponent experiences a sharp increase at about $\alpha=1$ and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For $\alpha<1$, 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 $\alpha>1$, the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.

Transport properties of inertial particles in networks with random long-range interactions

In this work, we investigate how the random long-range interactions (RLRIs) affect the directed transport properties of inertial particles in networks. The particles are driven by periodic time-dependent external forces, under the influence of an asymmetric periodic potential of the inertial ratchet type. First, transport of an arbitrary particle in the networks is studied and it is found that with the variation of topological randomness p defined as the fraction of RLRIs, the multiple current reversals take place. Secondly, cooperative directed transport of networks is explored. It is found that for the whole network, the optimum transport is achieved when topological randomness p=1. Finally, the possible mechanism underlying the RLRI-induced optimum transport is illustrated in terms of spatial synchronization of networks.

Quantum charge glasses of itinerant fermions with cavity-mediated long-range interactions

We study models of itinerant spinless fermions with random long-range interactions. We motivate such models from descriptions of fermionic atoms in multi-mode optical cavities. The solution of an infinite-range model yields a metallic phase which has glassy charge dynamics, and a localized glass phase with suppressed density of states at low energies. We compare these phases to the conventional disordered Fermi liquid, and the insulating electron glass of semiconductors. Prospects for the realization of such glassy phases in cold atom systems are discussed.

Random Long-Range Interaction Induced Synchronization in Coupled Networks of Inertial Ratchets

We investigate how the random long-range interactions affect the synchronization features in networks of inertial ratchets, where each ratchet is driven by a periodic time-dependent external force, under the influence of an asymmetric periodic potential. It is found that for a given coupling strength C, the synchronization of the coupled ratchets is induced as the fraction of random long-range interactions p increases and the ratchet networks reach full synchronization for a larger p. It is also found that the system reaches synchronization more effectively for a stronger coupling strength.

Exact solution of Ising model on a small-world network.

We present an exact solution of a one-dimensional Ising chain with both nearest-neighbor and random long-range interactions. Not surprisingly, the solution confirms the mean-field character of the transition. This solution also predicts the finite-size scaling that we observe in numerical simulations.

Small-world phenomena in physics: the Ising model

The Ising system with a small fraction of random long-range interactions is the simplest example of small-world phenomena in physics. Considering the latter both in an annealed and in a quenched state we conclude that: (a) the existence of random long-range interactions leads to a phase transition in the one-dimensional case and (b) there is a minimal average number p of these interactions per site (p<1 in the annealed state, and p1 in the quenched state) needed for the appearance of the phase transition. Note that the average number of these bonds, pN/2, is much smaller than the total number of bonds, N2/2.