Many-body localization in the presence of long-range interactions and long-range hopping

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) ∼ t0/r α with α < 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 < α < 2 delocalizes the system partially, with almost all the states extended for α ≤ 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.

Disordered Haldane-Shastry model

“…On the other hand, low entanglement and nonergodic behaviors, which are different from many-body localization, have been found in a nearest-neighbor model with SU(2) symmetry [16,17]. There were several studies investigating whether many-body localization can survive in the presence of different types of long-range terms in the Hamiltonian [33][34][35][36] since one might expect that long-range terms will increase the amount of entanglement. Similarly, it is unclear whether nonlocal terms will destroy the nonergodic, low entanglement behavior seen in local models with SU(2) symmetry.…”

“…There is currently much interest in finding out how nonlocal terms in a Hamiltonian affect the thermalization properties of a system [33][34][35][36], e.g., whether many-body localization is possible when different types of long-range terms are present, as one might expect that long-range terms could increase the amount of entanglement. As mentioned above, it has been argued that systems with SU(2) symmetry cannot many-body localize since SU(2) symmetry is incompatible with area law scaling of the entanglement entropy [14,15], and it is hence expected that we do not find many-body localization in the studied, nonlocal model.…”

Robustness of delocalization to the inclusion of soft constraints in long-range random models

“…Another intriguing question is how the interplay between partial correlations in hopping and interaction amplitudes could affect localization properties in many-body systems with either or both hopping and interaction terms being longranged in the coordinate space. Specifically, the limiting fullycorrelated case of the interacting version of Burin-Maksimov model was recently analyzed in [60,[72][73][74][75][76], and the opposite situation without any constraints was considered in details in [77][78][79][80][81][82]. However, the intermediate regime represented by both finite means and dispersion in distribution functions of matrix elements needs deep consideration.…”

d-Path Laplacians and Quantum Transport on Graphs

“…However, other theoretical frameworks used for disordered spin chain has shown the existence of MBL for strong LRI [36]. More recently, Nag and Garg [37] demonstrated that MBL persists in the presence strong long-range hopping. They studied a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions and long-range hopping.…”