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

Sebastian Schiffer; Jia Wang; Xia-Ji Liu; Hui Hu

doi:10.1103/PhysRevA.100.063619

paper

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

arXiv:1908.04031 · doi:10.1103/PhysRevA.100.063619

Abstract

We investigate the transition from the many-body localized phase to the ergodic thermalized phase at an infinite temperature in an $X Y$ spin chain with $L$ spins, which experiences power-law decaying interactions in the form of $V_{ij} \propto 1/ ∣ i - j ∣^{α}$ ( $i, j = 1, \dots, L$ ) 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 $L \to \infty$ . We find that both $W_{c}$ and $ν$ diverge when $α$ decreases to a critical power $α_{c} ≃ 1.16 \pm 0.17$ , 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 $α_{c} \approx 1$ from quantum dynamics simulation in Phys. Rev. A \textbf{99}, 033610 (2019).

arXiv comment9 pages, 9 figures

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

Abstract

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