Many-body localization in XY spin chains with long-range interactions: An exact-diagonalization study

We investigate the transition from the many-body localized phase to the ergodic thermalized phase at an infinite temperature in an XY spin chain with L spins, which experiences power-law decaying interactions in the form of V-ij alpha 1/vertical bar i - j vertical bar(alpha) (i, j = 1, ..., L) and a random transverse field. By performing large-scale exact diagonalization for the chain size up to L = 18, we systematically analyze the energy gap statistics, the half-chain entanglement entropy, and the uncertainty of the entanglement entropy of the system at different interaction exponents alpha. The finite-size critical scaling allows us to determine the critical disorder strength W-c and the critical exponent nu at the many-body-localization phase transition, as a function of the interaction exponent alpha in the limit L -> infinity. We find that both W-c and nu diverge when alpha decreases to a critical power of alpha(c) similar or equal to 1.16 +/- 0.17, indicating the absence of many-body localization for alpha < alpha(c). Our result differs from the analytical prediction of alpha(c) = 3/2 found in a previous work based on a scaling argument [A. L. Burin, Phys Rev. B 92. 104428 (2015)], but is close to the recent numerical result alpha(c) approximate to 1 obtained from quantum dynamics simulation [A. Safavi-Naini, M. L. Wall, O. L. Acevedo, A. M. Rey, and R. M. Nandkishore, Phys. Rev. A 99, 033610 (2019)].