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Physics Letters A

Identifying many-body localization transitions in a random-field Heisenberg chain via quantum nonlocality

Ziheng Liang, Jia Bao, Longhui Shen, Bin Guo, Zhao‐Yu Sun

Published Apr 3, 2023• 8 citations
Publisher
DOI
10.1016/j.physleta.2023.128810

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We investigate the many-body localization (MBL) transitions in a spin-1/2 Heisenberg chain with an on-site random magnetic field by employing global quantum discord (GQD). We use the disorder-averaged GQD to estimate the MBL critical point, which is found to be around atWc=3.8by making a finite-size scaling analysis. We further compare our results of GQD with those of half-chain entanglement entropy (EE) that is promising in the study of MBL. We show that GQD can exclude the finite-size interference under the same condition, which implies that GQD is more robust than the half-chain EE in characterizing MBL.
We study the many-body localization of the random-field Heisenberg chain using the nested shift-invert Lanczos method with an iterative linear solver. We use the minimum residual method (MINRES) inside each Lanczos iteration. The memory consumption of the proposed method is only proportional to the dimension of the Hilbert space. We also introduce a preconditioner that takes into account the effects of disorder and interaction in the random-field Heisenberg chain. As a probe of many-body localization transition, we propose a unitary operator called the twist operator, which has a clear interpretation in the real space. We discuss its behavior for thermal and localized eigenstates. We demonstrate the efficiency of the nested iterative shift-invert diagonalization method with the proposed preconditioner for the many-body localization problem and estimate the transition point of the random-field Heisenberg chain more precisely based on the finite-size analysis of the expectation value of the twist operator.