Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCan many-body localization persist in the presence of long-range interactions or long-range hopping?
66
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions or long-range hopping. Based on perturbative arguments there is a common belief that MBL can exist only in systems with short-range interactions and short-range hopping. We analyze effects of power-law interactions and power-law hopping, separately, on a system which has all the single particle states localized in the absence of interactions. Since delocalization is driven by proliferation of resonances in the Fock space, we mapped this model to an effective Anderson model on a complex graph in the Fock space, and calculated the probability distribution of the number of resonances up to third order. Though the most-probable value of the number of resonances diverge for the system with long-range hopping ($t(r) sim t_0/r^alpha$ with $alpha < 2$), there is no enhancement of the number of resonances as the range of power-law interactions increases. This indicates that the long-range hopping delocalizes the many-body localized system but in contrast to this, there is no signature of delocalization in the presence of long-range interactions. We further provide support in favor of this analysis based on dynamics of the system after a quench starting from a charge density wave ordered state, level spacing statistics, return probability, participation ratio and Shannon entropy in the Fock space. We demonstrate that MBL persists in the presence of long-range interactions though long-range hopping with $1<alpha <2$ delocalizes the system partially, with all the states extended for $alpha <1$. Even in a system which has single-particle mobility edges in the non-interacting limit, turning on long-range interactions does not cause delocalization.
rate research
Read More
We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions decaying as power-law $V_{ij}/(r_i-r_j)^alpha$ with distance and having random coefficients $V_{ij}$. We demonstrate that MBL survives even for $alpha <1$ and is preceded by a broad non-ergodic sub-diffusive phase. Starting from parameters at which the short-range interacting system shows 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 $alpha$. Hence, the critical disorder $h_c^r$, at which ergodic to non-ergodic transition takes place increases with the range of interactions. Time evolution of the density imbalance $I(t)$, which has power-law decay $I(t) sim t^{-gamma}$ in the intermediate to large time regime, shows that the critical disorder $h_{c}^I$, above which the system becomes diffusion-less (with $gamma sim 0$) 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 non-ergodic sub-diffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions and a non zero dynamical exponent $gamma ll 1/2$. The system continues to be sub-diffusive 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 super-diffusive with $gamma >1/2$. The rich phase diagram obtained here is unique to 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.
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.
While there are well established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power $alpha$, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing $alpha$. At $alpha_c$ the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many body localization transition in disordered antiferromagnetic spin chains with long range interactions.
Ergodicity in quantum many-body systems is - despite its fundamental importance - still an open problem. Many-body localization provides a general framework for quantum ergodicity, and may therefore offer important insights. However, the characterization of many-body localization through simple observables is a difficult task. In this article, we introduce a measure for distances in Hilbert space for spin-1/2 systems that can be interpreted as a generalization of the Anderson localization length to the many-body Hilbert space. We show that this many-body localization length is equivalent to a simple local observable in real space, which can be measured in experiments of superconducting qubits, polar molecules, Rydberg atoms, and trapped ions. Using the many-body localization length and a necessary criterion for ergodicity that it provides, we study many-body localization and quantum ergodicity in power-law-interacting Ising models subject to disorder in the transverse field. Based on the nonequilibrium dynamical renormalization group, numerically exact diagonalization, and an analysis of the statistics of resonances we find a many-body localized phase at infinite temperature for small power-law exponents. Within the applicability of these methods, we find no indications of a delocalization transition.
Many-body localization (MBL) behavior is analyzed {in an extended Bose-Hubbard model with quasiperiodic infinite-range interactions. No additional disorder is present. Examining level statistics and entanglement entropy of eigenstates we show that a significant fraction of eigenstates of the system is localized in the presence of strong interactions. In spite of this, our results suggest that the system becomes ergodic in the standard thermodynamic limit in which the energy of the system is extensive. At the same time, the MBL regime seems to be stable if one allows for a super-extensive scaling of the energy. We show that our findings can be experimentally verified by studies of time dynamics in many-body cavity quantum electrodynamics setups. The quench spectroscopy is a particularly effective tool that allows us to systematically study energy dependence of time dynamics and to investigate a mobility edge in our system.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
