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

Abstract

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 $V_{ij}\propto1/\left|i-j\right|^α$ ($i,j=1,\cdots,L$) 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, half-chain entanglement entropy, and uncertainty of the entanglement entropy of the system at different interaction exponents $α$. The finite-size critical scaling allows us to determine the critical disorder strength $W_{c}$ and critical exponent $ν$ at the many-body localization phase transition, as a function of the interaction exponent $α$ in the limit $L\rightarrow\infty$. We find that both $W_{c}$ and $ν$ diverge when $α$ decreases to a critical power $α_{c}\simeq1.16\pm0.17$, indicating the absence of many-body localization for $α<α_{c}$. Our result is useful to resolve the contradiction on the critical power found in two previous studies, $α_{c}=3/2$ from scaling argument in Phys. Rev. B \textbf{92}, 104428 (2015) and $α_{c}\approx1$ from quantum dynamics simulation in Phys. Rev. A \textbf{99}, 033610 (2019).