Eigenstate properties of the disordered Bose–Hubbard chain

IF 6.5 2区物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Frontiers of Physics Pub Date : 2024-03-01 DOI:10.1007/s11467-023-1384-1

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Abstract

Many-body localization (MBL) of a disordered interacting boson system in one dimension is studied numerically at the filling faction one-half. The von Neumann entanglement entropy S_vN is commonly used to detect the MBL phase transition but remains challenging to be directly measured. Based on the U(1) symmetry from the particle number conservation, S_vN can be decomposed into the particle number entropy S_N and the configuration entropy S_C. In light of the tendency that the eigenstate’s S_C nears zero in the localized phase, we introduce a quantity describing the deviation of S_N from the ideal thermalization distribution; finite-size scaling analysis illustrates that it shares the same phase transition point with S_vN but displays the better critical exponents. This observation hints that the phase transition to MBL might largely be determined by S_N and its fluctuations. Notably, the recent experiments [A. Lukin, et al., Science 364, 256 (2019); J. Léonard, et al., Nat. Phys. 19, 481 (2023)] demonstrated that this deviation can potentially be measured through the S_N measurement. Furthermore, our investigations reveal that the thermalized states primarily occupy the low-energy section of the spectrum, as indicated by measures of localization length, gap ratio, and energy density distribution. This low-energy spectrum of the Bose model closely resembles the entire spectrum of the Fermi (or spin XXZ) model, accommodating a transition from the thermalized to the localized states. While, owing to the bosonic statistics, the high-energy spectrum of the model allows the formation of distinct clusters of bosons in the random potential background. We analyze the resulting eigenstate properties and briefly summarize the associated dynamics. To distinguish between the phase regions at the low and high energies, a probing quantity based on the structure of S_vN is also devised. Our work highlights the importance of symmetry combined with entanglement in the study of MBL. In this regard, for the disordered Heisenberg XXZ chain, the recent pure eigenvalue analyses in [J. Suntajs, et al., Phys. Rev. E 102, 062144 (2020)] would appear inadequate, while methods used in [A. Morningstar, et al., Phys. Rev. B 105, 174205 (2022)] that spoil the U(1) symmetry could be misleading. Abstract Image

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无序玻色-哈伯德链的特征态特性

摘要在填充派二分之一处对一维无序相互作用玻色子系统的多体局域化（MBL）进行了数值研究。冯-诺依曼纠缠熵 SvN 通常用于探测 MBL 相变，但直接测量它仍然具有挑战性。基于粒子数守恒的 U(1) 对称性，SvN 可分解为粒子数熵 SN 和构型熵 SC。鉴于特征态的 SC 在局部化阶段趋近于零，我们引入了一个描述 SN 与理想热化分布偏差的量；有限尺寸缩放分析表明，它与 SvN 具有相同的相变点，但显示出更好的临界指数。这一观察结果表明，向 MBL 的相变可能在很大程度上取决于 SN 及其波动。值得注意的是，最近的实验 [A. Lukin, et al.Lukin, et al., Science 364, 256 (2019)；J. Léonard, et al., Nat.19，481 (2023)]表明，这种偏差有可能通过 SN 测量来测量。此外，我们的研究还发现，热化态主要占据了光谱的低能段，这一点可以从局域化长度、间隙比和能量密度分布的测量结果中看出。玻色模型的这一低能光谱与费米（或自旋 XXZ）模型的整个光谱非常相似，包含了从热化态到局域态的过渡。同时，由于玻色子统计，该模型的高能谱允许在随机势背景中形成不同的玻色子簇。我们分析了由此产生的特征态特性，并简要总结了相关动力学。为了区分低能和高能的相区，我们还设计了一种基于 SvN 结构的探测量。我们的工作凸显了对称性与纠缠结合在 MBL 研究中的重要性。在这方面，对于无序的海森堡 XXZ 链，最近[J. Suntajs 等，Phys. Rev. E 102, 062144 (2020)]中的纯特征值分析似乎不够充分，而[A. Morningstar 等，Phys. Rev. B 105, 174205 (2022)]中使用的破坏 U(1) 对称性的方法可能会产生误导。

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来源期刊

Frontiers of Physics PHYSICS, MULTIDISCIPLINARY-

CiteScore

9.20

自引率

9.30%

发文量

898

审稿时长

6-12 weeks

期刊介绍： Frontiers of Physics is an international peer-reviewed journal dedicated to showcasing the latest advancements and significant progress in various research areas within the field of physics. The journal's scope is broad, covering a range of topics that include: Quantum computation and quantum information Atomic, molecular, and optical physics Condensed matter physics, material sciences, and interdisciplinary research Particle, nuclear physics, astrophysics, and cosmology The journal's mission is to highlight frontier achievements, hot topics, and cross-disciplinary points in physics, facilitating communication and idea exchange among physicists both in China and internationally. It serves as a platform for researchers to share their findings and insights, fostering collaboration and innovation across different areas of physics.