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 Vij ∝ 1/ |i − j| α (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, 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 Wc and critical exponent ν at the many-body localization phase transition, as a function of the interaction exponent α in the limit L → ∞. We find that both Wc and ν diverge when α decreases to a critical power αc 1.16 ± 0.17, indicating the absence of many-body localization for α < αc. Our result is useful to resolve the contradiction on the critical power found in two previous studies, αc = 3/2 from scaling argument in Phys. Rev. B 92, 104428 (2015) and αc ≈ 1 from quantum dynamics simulation in Phys. Rev. A 99, 033610 (2019). arXiv:1908.04031v2 [cond-mat.quant-gas]

Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain

“…The finite-size scaling analysis of the MBL transition was first made as if it were a standard secondorder phase transition, with a behavior of the type y = y c F (L/ξ) (where y is the observable and y c = y(L, h c )) with ξ a characteristic length diverging algebraically at the transition ξ ∼ |h − h c | −ν . Many works converged on a critical exponent ν ≈ 1 [23,29,[32][33][34][35]. This value of the critical exponent contradicts the Harris criterion [51,52].…”

“…A more serious issue concerns the universality class of the ergodic-MBL transition, for which numerical simulations yield a localization length ξ ∼ |h−h c | −ν with an exponent ν ≈ 1 for both sides of the transition [23,29,[32][33][34][35]. Only recently, a finite-size scaling analysis of the multifractal properties has found an asymmetric criticality for the multifractal dimension [36], thus making an interesting connection with the Anderson problem on random graphs [37][38][39][40][41][42][43][44][45][46][47][48][49][50] where such unusual scaling properties were first found [45,49].…”

Quantum entanglement, local indicators, and the effect of external fields in the Kugel-Khomskii model

“…Here, we use the so called "concurrence". Naturally, since we use the exact diagonalization of the Hamiltonian [32][33][34][35][36] method, any other criterion can also be calculated.…”

Continuous dynamical decoupling of spin chains: Inducing two-qubit interactions to generate perfect entanglement

“…Several studies have focused on studying entanglement and quantum correlations in different types of spin chains. Many body localization in XY spin chains using exact diagonalization method has been studied in [9], while [10] studies entanglement and correlations in a onedimensional quantum spin chain with anisotropic powerlaw long-range interactions. Moreover, achieving entanglement over arbitrarily long distances in a spin chain has been a long-standing goal and a focus of many studies.…”