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 $V_{ij}\propto 1/{\left|i-j\right|}^{\alpha }$ ($i,j=1,\cdots ,L$) 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 $\alpha$. The finite-size critical scaling allows us to determine the critical disorder strength $W_c$ and critical exponent $\nu$ at the many-body localization phase transition, as a function of the interaction exponent $\alpha$ in the limit $L\to \infty$. We find that both $W_c$ and $\nu$ diverge when $\alpha$ decreases to a critical power ${\alpha }_c\simeq 1.16\pm 0.17$, indicating the absence of many-body localization for $\alpha <{\alpha }_c$. Our result is useful to resolve the contradiction on the critical power found in two previous studies, ${\alpha }_c=3/2$ from scaling argument in Phys. Rev. B \textbf{92}, 104428 (2015) and ${\alpha }_c\approx 1$ from quantum dynamics simulation in Phys. Rev. A \textbf{99}, 033610 (2019).

9 pages, 9 figures